Question

question 34 of 40 given circle x with radius 10 units and chord ab with length 12 units, what is the length of segment cx, which bisects the chord? a. 8 units b. 16 units c. 10 units d. 6 units

Explanation:

Step1: Recall chord - bisecting property

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 of the circle and $CB$ is half of the chord $AB$.

Step2: Calculate the length of $CB$

Since $AB = 12$ units and $CX$ bisects $AB$, then $CB=\frac{AB}{2}=\frac{12}{2}=6$ units. The radius $XB = 10$ units.

Step3: Use the Pythagorean theorem

In right - triangle $\triangle{XCB}$, by the Pythagorean theorem $CX=\sqrt{XB^{2}-CB^{2}}$. Substitute $XB = 10$ and $CB = 6$ into the formula: $CX=\sqrt{10^{2}-6^{2}}=\sqrt{100 - 36}=\sqrt{64}=8$ units.

Answer:

A. 8 units