Question

The perpendicular bisector of a chord XY cuts
XY at N and the circle at P. Given that XY = 16 cm
and NP = 2 cm, calculate the radius of the circle.​

Answer 1

Answer:

The perpendicular bisector of a chord XY cuts XY at N and the circle at P. If XY=16 cm and NP=2cm, calculate he radius of the circle. The answer to this question is 17cm, but I can't solve it.

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Answer 2

Answer: 17 cm

Step-by-step explanation:

Follow the image for the solution.

Let O be the center of the circle.

Since NP is the perpendicular bisector of XY,

XN = YN = 8 cm

Connect points O and Y using a straight line.

Apply Pythagoras theorem to triangle ONY.

$\begin{aligned}(OY)^2&=(ON)^2+(YN)^2\\(OY)^2&=(OP-PN)^2+8^2\\(OY)^2&=(OY-2)^2+64\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(\because OP=OY=\text{radius})\end{aligned}$

Let OY be r. Solve further.

$\begin{aligned}(r)^2&=(r-2)^2+64\\r^2&=r^2-4r+4+64\\4r&=68\\r&=17\,\rm{cm}\end{aligned}$