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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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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,
ЁЭСГЁЭСД2 + ЁЭСВЁЭСГ2 = ЁЭСВЁЭСД2
⇒ 242 + ЁЭСВЁЭСГ2 = 252
⇒`PO = sqrt((25)^2 − (24)^2) = sqrt(625 − 576)`
= `sqrt(49)` = 7ЁЭСРЁЭСЪ
∴ ЁЭСВЁЭСГ = ЁЭСЯЁЭСОЁЭССЁЭСЦЁЭСвЁЭСа = 7ЁЭСРЁЭСЪ
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