Question

Chords AB and CD of a circle are produced to meet at the point P, outside the circle, and AD is the diameter of the circle. If ∠DAP = 36° and ∠APC = 30°, then what will be the measure of ∠CBD?
1. 34°
2. 26°
3. 24°
4. 16°

Answer 1

Correct Answer - Option 3 : 24°

Given:

∠DAP = 36° 

∠APC = 30° 

Calculation:

According to the question

⇒ ∠CDB = ∠DAP + ∠APC + 90°  

⇒ ∠CDB = 36° + 30° + 90° 

⇒156° 

⇒ ∠CDB =156° 

Now, in ΔCBA

⇒ ∠CBD = 180° – 156° 

⇒ ∠CBD = 24° 

∴ The required value of ∠CBD = 24°