Question

If the tangent at point P to the circle with center O cuts a line through O at Q such that PQ = 24 cm and OQ = 25 cm. Find the radius of circle.

Answer 1

Given,

PQ = 24 cm

OQ = 25 cm

OP = radius = ?

P is point of contact, At point of contact, tangent and radius are perpendicular to each other

∴ ΔPOQ is right angled triangle ∠OPQ = 90°

By Pythagoras theorem,

𝑃𝑄² + 𝑂𝑃² = 𝑂𝑄²

⇒ 24² + 𝑂𝑃² = 25²

⇒`PO = sqrt((25)^2 − (24)^2) = sqrt(625 − 576)`

= `sqrt(49)` = 7𝑐𝑚

∴ 𝑂𝑃 = 𝑟𝑎𝑑𝑖𝑢𝑠 = 7𝑐𝑚