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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

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#### 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,

𝑃𝑄^{2} + 𝑂𝑃^{2} = 𝑂𝑄^{2}

⇒ 24^{2} + 𝑂𝑃^{2} = 25^{2}

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

= `sqrt(49)` = 7𝑐𝑚

∴ 𝑂𝑃 = 𝑟𝑎𝑑𝑖𝑢𝑠 = 7𝑐𝑚

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