Question:
From a point Q, the length of the tangent to a circle is 24 cm and the distance of Q from the centre is 25 cm. The radius of the circle is (A) 7 cm (B) 12 cm (C) 15 cm (D) 24.5 cm
Answer:
Given length of tangent AB = 24 cm
Distance from centre of the circle to point B = 25 cm
Let OA is the radius of the circle.
Now from Pythagoras Theorem,
OB2 = OA2 + AB2
=> 252 = OA2 + 242
=> 625 = OA2 + 576
=> OA2 = 625 - 576
=> OA2 = 49
=> OA = √49
=> OA = 7
So radious of the circle = 7 cm
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