Question

question 7 of 33 given circle x with radius 17 units and chord ab with length 30 units, what is the length of segment xc, which bisects the chord? a. 8 units b. 2 units c. 5 units d. 25 units

Explanation:

Step1: Recall the property of a line bisecting a chord

A line from the center of a circle that bisects a chord is perpendicular to the chord. So triangle $XCB$ is a right - triangle, where $XB$ is the radius and $BC$ is half of the chord length.

Step2: Calculate the length of $BC$

Since chord $AB = 30$ units and $XC$ bisects $AB$, then $BC=\frac{AB}{2}=\frac{30}{2}=15$ units. The radius $XB = 17$ units.

Step3: Apply the Pythagorean theorem

In right - triangle $XCB$, by the Pythagorean theorem $XC=\sqrt{XB^{2}-BC^{2}}$. Substitute $XB = 17$ and $BC = 15$ into the formula: $XC=\sqrt{17^{2}-15^{2}}=\sqrt{(17 + 15)(17 - 15)}=\sqrt{32\times2}=\sqrt{64}=8$ units.

Answer:

A. 8 units