Question

1. in which type of triangle is the incenter also the circumcenter? a. equilateral triangle b. scalene triangle c. obtuse triangle d. right triangle 5. what happens if two tangent lines intersect outside a circle? a. they are perpendicular to the radius b. they are parallel c. they form a right angle d. they create congruent segments from the point of intersection to the points of tangency 6. which is not a point of concurrency in a triangle? a. midpoint of a side b. circumcenter c. incenter d. centroid

Explanation:

• For question 4: In an equilateral triangle, due to its symmetry, the in - center (center of the inscribed circle) and the circum - center (center of the circumscribed circle) coincide.
• For question 5: When two tangent lines intersect outside a circle, the segments from the point of intersection to the points of tangency are congruent, which is a well - known property of circle tangents.
• For question 6: Points of concurrency in a triangle are the circumcenter (intersection of perpendicular bisectors), incenter (intersection of angle bisectors), and centroid (intersection of medians). The mid - point of a side is not a point of concurrency.

Answer:

1. a. Equilateral triangle
2. d. They create congruent segments from the point of intersection to the points of tangency
3. a. Midpoint of a side