SSC CGL 24 Aug 2021 Shift 3 Paper

Question : 55 of 100

Marks: +1, -0

In a circle with centre

O

, points

A, B

C

and

D

in this order are concyclic such that

B D

is a diameter of the circle. If

∠ B A C=22^{∘}

, then find the measure (in degrees) of

∠ C O D

Solution:

Given,

B D=

Diameter

∠ B A C=22^{∘}

Angles subtended by the same arc at the circumference are equal.

So,

\;\; ∠ B A C=∠ B D C=22^{∘}

△ B C D

∠ B C D+∠ C D B+∠ D B C=180^{∘}

⇒ \;\; ∠ 0^{∘}+22^{∘}+∠ D B C=180^{∘}

⇒ \;\; ∠ D B C=180^{∘}-90^{∘}-22^{∘}=68^{∘}

\;\text " We know that, "\; ∠ C O D=2 ∠ D B C

∠ C O D=2 × 68^{∘}=136^{∘}

∠ C O D=136^{∘}

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