a. draw an inscribed right angle in circle t. label each point where the angle intersects the circle.
enter the answer in each space provided. use numbers instead of words.
what is the name of the right angle?

b. draw the chord determined by the inscribed right angle.
enter the answer in the space provided. use numbers instead of words.
what is the name of the chord?

c. draw a different inscribed right angle in circle t using points not used in part (a). label each point where the

Question

a. draw an inscribed right angle in circle t. label each point where the angle intersects the circle.
> enter the answer in each space provided. use numbers instead of words.
what is the name of the right angle?

b. draw the chord determined by the inscribed right angle.
> enter the answer in the space provided. use numbers instead of words.
what is the name of the chord?

c. draw a different inscribed right angle in circle t using points not used in part (a). label each point where the

Accepted Answer

### Part (a)
# Explanation:
To form an inscribed right angle in a circle, we can use the property that an angle inscribed in a semicircle is a right angle. Let's assume we choose two points on the circle and a third point such that the angle is right. If we take points, say, $ A $, $ B $ (a new point) and $ C $ (another new point), but more simply, using the given circle with center $ T $, if we have a diameter (which we can form), the angle subtended by the diameter is a right angle. Let's say we have points $ A $, $ B $ (on the circle) and the right angle is $ \angle ABC $ but more appropriately, if we take two points on the circle and the right angle is at a point on the circle. Wait, actually, the inscribed right angle should have its vertex on the circle and the sides intersecting the circle at two other points. So if we have a circle with center $ T $, and we draw a right angle with vertex at, say, $ A $ (on the circle) and the other two points $ B $ and $ C $ on the circle, but the key is that the hypotenuse of the right - angled triangle (the chord opposite the right angle) is a diameter. But for the name of the right angle, if we have points $ A $, $ B $, and $ C $ on the circle with $ \angle ABC = 90^\circ $, but in the given circle, let's assume we have points $ A $, $ E $, and another point, say $ D $. Wait, maybe a better approach: the inscribed right angle can be named as $ \angle AED $ (but we need to use the points. Wait, the circle has center $ T $, and point $ A $ and $ E $ are on the circle. Let's say we draw a right angle with vertex at a point, say, $ A $, and the other two points $ B $ (a new point) and $ C $ (another new point), but the problem says "use numbers instead of words" no, wait, the problem says "label each point where the angle intersects the circle" and "enter the answer in each space provided. Use numbers instead of words" - no, maybe it's a typo, and we can use letters. Wait, the circle has center $ T $, point $ A $ and $ E $ are on the circle. Let's assume that we form a right angle with vertex at a point, say, $ A $, and the other two points $ B $ and $ C $ on the circle, but actually, the correct way is that if we have a diameter, the angle subtended by the diameter is a right angle. So if we have a diameter, say, $ AE $ (but $ AE $ is not a diameter, $ TA $ and $ TE $ are radii). Wait, maybe the right angle is $ \angle ADE $ where $ D $ is a point on the circle. But maybe a simpler way: the inscribed right angle can be named as $ \angle ABE $ (but we need to define the points. Alternatively, if we take three points on the circle $ A $, $ B $, $ C $ such that $ \angle ABC = 90^\circ $, and the chord $ AC $ is the diameter. But in the given circle, let's assume that the right angle is $ \angle ADE $ with $ D $ and $ E $ on the circle, but the problem says "label each point where the angle intersects the circle". So the right angle will have its vertex on the circle and two sides intersecting the circle at two other points. So the name of the right angle could be $ \angle AFE $ (where $ F $ and $ E $ are on the circle and $ A $ is the vertex), but maybe a more concrete example: if we have a circle, and we draw a right angle with vertex at $ A $ (on the circle) and the other two points $ B $ and $ C $ on the circle, the angle is $ \angle ABC $ (vertex at $ B $)? Wait, no, the vertex of the angle is on the circle. So the right angle is named by its vertex and the two points where the sides intersect the circle. So if the vertex is $ A $, and the sides intersect the circle at $ B $ and $ C $, the angle is $ \angle BAC $. But since the problem says "use numbers instead of words" - maybe it's a mistake, and we can use letters. Let's assume that we have a right angle with vertex at a point on the circle, say $ A $, and the other two points $ B $ and $ C $ on the circle, so the angle is $ \angle ABC $ (vertex at $ B $)? No, I think the key property is that the inscribed right angle's hypotenuse is a diameter. So if we draw a diameter, say, $ AE $ (but $ AE $ is not a diameter, $ TA $ and $ TE $ are radii). Wait, maybe the circle has points $ A $, $ E $, and we can add a point $ D $ such that $ \angle ADE = 90^\circ $, and the chord $ AE $ is the diameter. Wait, maybe the right angle is $ \angle ADE $ with $ D $ on the circle, $ A $ and $ E $ on the circle. So the name of the right angle is $ \angle ADE $ (but we need to check the points. Alternatively, if we take two points on the circle, say $ A $ and $ E $, and a third point $ B $ on the circle, then $ \angle ABE = 90^\circ $ if $ AE $ is a diameter. So the name of the right angle could be $ \angle ABE $. But since the problem is about drawing, and the answer for the name of the right angle (assuming we have points $ A $, $ B $, $ C $ on the circle with $ \angle ABC = 90^\circ $) - but maybe a better approach: the inscribed right angle is formed by three points on the circle, with the right angle at one of the points. So if we have a circle, and we draw a right angle with vertex at, say, $ A $, and the other two points $ B $ and $ C $ on the circle, the angle is $ \angle BAC $. But the problem says "use numbers instead of words" - maybe it's a misstatement, and we can use letters. Let's assume that the right angle is $ \angle ADE $ where $ D $ is a point on the circle, $ A $ and $ E $ are on the circle. So the name of the right angle is $ \angle ADE $.
## Step 1: Recall the property of inscribed angles
An angle inscribed in a semicircle is a right angle. So we need to find three points on the circle such that one of the angles formed is a right angle, with the vertex on the circle and the other two points on the circle.
## Step 2: Name the right angle
Let's assume we have points $ A $, $ D $, and $ E $ on the circle, with $ \angle ADE = 90^\circ $. So the name of the right angle is $ \angle ADE $ (or any other valid inscribed right angle name based on the circle's points). But since the circle has center $ T $ and points $ A $ and $ E $ on it, a possible right angle is $ \angle AFE $ (where $ F $ is a point on the circle) with $ \angle AFE = 90^\circ $ and $ AE $ as the diameter. So the name of the right angle is $ \angle AFE $ (assuming $ F $ is a point on the circle). But if we consider the standard, the right angle can be named as $ \angle ABC $ where $ B $ is on the circle, $ A $ and $ C $ are on the circle and $ AC $ is a diameter.
# Answer (a):
$ \angle ADE $ (or other valid inscribed right - angle name based on the circle's points. If we assume points $ A $, $ B $, $ C $ with $ \angle ABC = 90^\circ $, it can be $ \angle ABC $)

### Part (b)
# Explanation:
The chord determined by the inscribed right angle is the chord that is opposite the right angle (the hypotenuse of the right - angled triangle). Since the inscribed right angle is subtended by a diameter (by the property of inscribed angles in a circle), the chord is the diameter. If the right angle is $ \angle ADE $ with $ A $ and $ E $ on the circle, then the chord is $ AE $.
## Step 1: Recall the property of inscribed right angles
The hypotenuse of a right - angled triangle inscribed in a circle is the diameter of the circle. So the chord opposite the right angle (the hypotenuse) is a diameter.
## Step 2: Determine the chord
If the inscribed right angle has its sides intersecting the circle at points $ A $ and $ E $ (and the vertex at another point on the circle), then the chord determined by the inscribed right angle is $ AE $.
# Answer (b):
$ AE $

### Part (c)
# Explanation:
To draw a different inscribed right angle, we need to use points not used in part (a). Let's assume in part (a) we used points $ A $, $ E $, and $ D $. We can choose new points, say, $ B $, $ C $, and $ F $ on the circle such that $ \angle BCF = 90^\circ $. The vertex $ F $ is on the circle, and $ B $ and $ C $ are new points on the circle (not $ A $ or $ E $). We label the points: $ B $ (on the circle), $ C $ (on the circle), and $ F $ (on the circle) where $ \angle BCF = 90^\circ $. The key is to use the property that the angle subtended by a diameter is a right angle, so we can draw a new diameter (using new points) and then place the right - angle vertex on the circle.
## Step 1: Choose new points
Select two new points $ B $ and $ C $ on the circle (not used in part (a)) and a third point $ F $ on the circle such that $ \angle BCF = 90^\circ $.
## Step 2: Label the points
Label the vertex of the right angle as $ F $ and the other two points as $ B $ and $ C $ on the circle.
# Answer (c):
(The drawing would involve a right angle with vertex at a new point on the circle, say $ F $, and the other two points $ B $ and $ C $ on the circle, with $ \angle BCF = 90^\circ $. The points are labeled as $ B $, $ C $ (intersection points of the angle's sides with the circle) and $ F $ (the vertex of the right angle on the circle).)

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QUESTION IMAGE

Question

Explanation:

Part (a)

Step 1: Recall the property of inscribed right angles

Step 2: Determine the chord

Step 1: Choose new points

Step 2: Label the points

Answer:

Part (b)