A chord of length 20 cm makes an angle of 90° at the center of a circle. Find the radius of the circle and the distance of this chord from the center.
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Correct answer: D
Explanation
Given:
Chord = 20 cm, Angle at the center = 90°
According to the formulas:
Chord = 2r sin(θ/2)
Distance from the center = r cos(θ/2)
20 = 2r sin 45°
20 = 2r × (1/√2)
20 = r√2
r = 20/√2 = 10√2
Distance from the center = r cos 45°
= 10√2 × (1/√2) = 10
Radius = 10√2 cm, Distance = 10 cm