On a circular path of radius 6 m a boy starts from a point \(A\) on the circumference and walks along a chord \(AB\) of length 3 m. He then walks along another chord \(BC\) of length 2 m to reach…
Question and options
On a circular path of radius 6 m a boy starts from a point on the circumference and walks along a chord of length 3 m. He then walks along another chord of length 2 m to reach point . The point lies on the minor arc . The distance of point from point is
- m
- m
- m
- m
Answer and explanation
Correct answer: A - \(\frac{\sqrt{15} + \sqrt{35}}{2}\) m
Chord = 2R sin(inscribed angle): sin a = 3/12 = 1/4, sin b = 2/12 = 1/6. Since B is on minor arc AC, AC = 12 sin(a+b) = 12[(1/4)(sqrt35/6) + (sqrt15/4)(1/6)] = (sqrt15 + sqrt35)/2 m.
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