#### Question

In the given figure, XY is the diameter of the circle and PQ is a tangent to the circle at Y.

If ∠AXB = 50° and ∠ABX = 70° and ∠BAY and ∠APY

#### Solution

In ΔAXB,

`∠`XAB + `∠`AXB + `∠`ABX=180° [Triangle property]

⇒ `∠`XAB + 50° + 70° = 180°

⇒ `∠`XAB = 180° − 120° = 60°

⇒ `∠`XAY=90° [Angle of semi-circle]

∴ `∠`BAY = `∠`XAY − `∠`XAB = 90° − 60° = 30°

and `∠`BXY = `∠`BAY = 30° [Angle of same segment]

`∠`ACX = `∠` BXY + `∠`ABX [External angle = Sum of two interior angles]

= 30° + 70°

= 100°

also,

`∠`XYP = 90° [Diameter ⊥ tangent]

`∠` APY = `∠`ACX − `∠`CYP

`∠`APY = 100° − 90°

`∠`APY = 10°

Is there an error in this question or solution?

Solution In the Given Figure, Xy is the Diameter of the Circle and Pq is a Tangent to the Circle at Y. If ∠Axb = 50° and ∠Abx = 70° and ∠Bay and ∠Apy Concept: Tangent Properties - If a Line Touches a Circle and from the Point of Contact, a Chord is Drawn, the Angles Between the Tangent and the Chord Are Respectively Equal to the Angles in the Corresponding Alternate Segments.