Question

In the given figure, C is the centre of the circle. seg QT is a diameter CT = 13, CP = 5, find the length of chord RS.

Answer 1

Draw seg CR

CR = CT = 13      ...(radii of the same circle)

In ΔCPR, ∠CPR = 90°

From Pythagoras' theorem,

CR² = CP² + PR²

∴ 13² = 5² + PR²

∴ 169 = 25 + PR²

∴ PR² = 169 – 25

∴ PR² = 144

∴ PR = ${\displaystyle \sqrt{144}}$

∴ PR = 12 cm

Now, seg CP ⊥ chord RS

∴ PR = ${\displaystyle \frac{1}{2}}$ RS       ...(The perpendicular drawn from the center of the circle to the chord bisects the chord.)

∴ 12 = ${\displaystyle \frac{1}{2}}$ RS

∴ RS = 12 × 2

∴ RS = 24