#### 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:

(i) ∠BAP (ii) ∠ABD (iii) ∠QAD (iv) ∠BCD

#### Solution

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°

Is there an error in this question or solution?

Solution In the Given Figure, Qap is the Tangent at Point a and Pbd is a Straight Line. If ∠Acb = 36° and ∠Apb = 42°, Find: (I) ∠Bap (Ii) ∠Abd (Iii) ∠Qad (Iv) ∠Bcd Concept: Chord Properties - a Straight Line Drawn from the Center of a Circle to Bisect a Chord Which is Not a Diameter is at Right Angles to the Chord.