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In the figure Δ ABC is inscribed in a circle with center O. If ∠ ABC is two times of ∠ BCA, then find the ∠ BCA.

In the figure Δ ABC is inscribed in a circle with center O. If ∠ ABC is two times of ∠ BCA, then find the ∠ BCA. Correct Answer 30° 

Given:

∠ ABC = 2 × ∠ BCA

BC is a diameter.

Concept Used:

The angle subtended by semicircle is a right angle.

Calculation:

∠ BAC = 90° 

In Δ ABC 

∠ ABC + ∠ BAC + ∠ BAC = 180° 

⇒ 2(∠ BCA) + ∠ BAC  + 90° = 180° 

⇒ 3 × ∠ BCA = 180°  – 90°  

⇒ 3 × ∠ BCA = 90° 

⇒ ∠ BCA = 90/3

⇒ ∠ BCA = 30° 

∴ ∠ BCA is 30°. 

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