GATE EE 2020 Set 1 — Question 9
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General Aptitude → Quantitative Aptitude → Mensuration & Geometry
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Question
Given a semicircle with as the centre, as shown in the figure, the ratio is ———, where , and are chords.

Correct answer
(A) √(2)
Solution
From the figure, is the center of the semicircle and is the diameter. Let the radius be . Thus, and .
The figure shows . In the right-angled triangle :
Similarly, in the right-angled triangle :
The required ratio is:
The figure shows . In the right-angled triangle :
Similarly, in the right-angled triangle :
The required ratio is:
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