Question

In the given figure, QAP is the tangent at point A and PBD is a straight line.

If ∠ACB = 36° and ∠APB = 42°, find:

1. ∠BAP
2. ∠ABD
3. ∠QAD
4. ∠BCD

Answer 1

PAQ is a tangent and AB is a chord of the circle.

i. ∴ ∠BAP = ∠ACB = 36°  ...(Angles in alternate segment)

ii. In ΔAPB

Ext ∠ABD = ∠APB + ∠BAP

`=>` Ext ∠ABD = 42° + 36° = 78°

iii. ∠ADB = ∠ACB = 36°  ...(Angles in the same segment)

Now in ΔPAD

Ext. ∠QAD = ∠APB + ∠ADB

`=>` Ext ∠QAD = 42° + 36° = 78°

iv. PAQ is the tangent and AD is chord

∴ QAD = ∠ACD = 78°  ...(Angles in alternate segment)

And ∠BCD = ∠ACB + ∠ACD

∴  ∠BCD = 36° + 78° = 114°