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
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°
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.