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Angle in a Semicircle

If R 1 and R ...

Question

If R1 and R2 are two congruent circles with BD and CE as diameters , then find which angle is equal to 30°.

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Solution

The correct option is A
Given that, R1 and R2 are congruent circles with A and B as centre.
$∴$ If we create $△$ ABC , it will be an equilateral triangle ,since all the sides are radii of 2 congruent circles.
$∴ ∠ C A B = ∠ A B C = ∠ B C A = 60 °$

A triangle inscribed in a semi circle with its diameter as the largest side will always be a right angled triangle.
$∴ ∠ D C B = 90 °$

$∠ C A D = 180 ° - ∠ C A B = 120 °$
[ $∵ ∠ C A B a n d ∠ C A D$ are supplementary angles]

Angle subtended by an arc at the centre is double the angle subtended at the circumference.
$∴ ∠ C D B = \frac{1}{2} ∠ C A B = \frac{1}{2} \times 60 ° = 30 °$

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