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Question
If the tangent at point P to the circle with center O cuts a line through O at Q such that PQ= 24cm and OQ = 25 cm. Find the radius of circle
Solution
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,
๐๐2 + ๐๐2 = ๐๐2
⇒ 242 + ๐๐2 = 252
⇒`PO = sqrt((25)^2 − (24)^2) = sqrt(625 − 576)`
= `sqrt(49)` = 7๐๐
∴ ๐๐ = ๐๐๐๐๐ข๐ = 7๐๐
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