Question

Please answer this multiple choice question!

Answer 1

`\large\boxed{d.\ 11.3\ cm}`

Explanation:

Look at the picture.

CQ is a perpendicular bisector of PR. Therefore QR = QP.

`PR=16\ cm\to QP = 16 cm : 2 = 8\ cm`

The segment CP is a radius of the given circle.

We have the right triangle CQP. Use the Pythagorean theorem:

`CQ^2+QP^2=CP^2`

Substitute CQ = 8 cm and QP = 8 cm.

`CP^2=8^2+8^2\\\\CP^2=64+64\\\\CP^2=128\to CP=√(128)\\\\CP\approx11.3\ cm`

Answer 2

d. 11.3 cm

Explanation:

The radius of the circle is the length CP, which can be found using the Pythagorean theorem. Since CQ ⊥ PR, you know that Q is the midpoint of PR and PQ = 8 cm.

Then the Pythagorean theorem tells you ...

CP² = CQ² +PQ² = (8 cm)² + (8 cm)² = 128 cm²

CP = √128 cm = 8√2 cm

CP = 11.3 cm