Find the diameter of a circle, if the length of the tangent is 9 m and 12 m is the distance between the center of the circle to the external point. Given √7 = 2.64 (approx)
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Correct answer: C
Explanation
Given:
Length of tangent = 9 m
Distance from center to external point = 12 m
Since the tangent to a circle is always perpendicular to the radius at the point of tangency, the tangent, the radius, and the line from the center to the external point together form a right triangle, in which the distance from the center to the external point is the hypotenuse.
By Pythagoras theorem:
(tangent)² + (radius)² = (distance from center)²
9² + r² = 12²
81 + r² = 144
r² = 144 − 81 = 63
r = √63 = √(9 × 7) = 3√7
Substituting √7 = 2.64:
r = 3 × 2.64 = 7.92 m
Diameter:
d = 2r = 2 × 7.92 = 15.84 m
Hence, the diameter of the circle = 15.84 m