Mathematics
In the given figure, AB is diameter and PC is tangent to the circle with center O. If AP = 40 cm, CP = 20 cm, find the radius of the circle.
Circles
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Answer
Let radius of circle be r cm.
From figure,
⇒ AP = AB + BP
⇒ 40 = AO + OB + BP
⇒ 40 = r + r + BP
⇒ 40 = 2r + BP
⇒ BP = (40 - 2r) cm.
We know that,
Tangent at point of intersection and radius of circle are perpendicular to each other.
In △OCP,
⇒ OP2 = OC2 + PC2
⇒ (OB + BP)2 = OC2 + PC2
⇒ (r + 40 - 2r)2 = r2 + 202
⇒ (40 - r)2 = r2 + 400
⇒ 1600 + r2 - 80r = r2 + 400
⇒ r2 - r2 + 80r = 1600 - 400
⇒ 80r = 1200
⇒ r = = 15 cm.
Hence, radius of circle = 15 cm.
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