Question

The radii of two concentric circles are 17 cm and 10 cm. A line segment PQRS cuts outer circle at P and S and inner circle at Q and R. If QR = 12 cm, find the length of PQ.

Answer 1

Step 1:

Let M be the midpoint of QR

`QM = (QR)/2`

= `12/2`

= 6 cm

In right triangle OMQ,

OM² + QM² = OQ²

OM² + 6² = 10²

OM² = 100 – 36 = 64

OM = `sqrt(64)` = 8 cm

Step 2:

In right triangle OMP,

OM² + PM² = OP²

8² + PM² = 17²

PM² = 289 – 64 = 225

PM = `sqrt(225)` = 15 cm

Step 3:

PQ = PM – QM

PQ = 15 – 6 = 9 cm

The length of PQ is 9 cm.