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Two tangents AP and AQ are drawn to a circle with centre O from external point A, where P and Q are points on circle. if ∠ PAQ = 70° then ∠ AOP = ?

Two tangents AP and AQ are drawn to a circle with centre O from external point A, where P and Q are points on circle. if ∠ PAQ = 70° then ∠ AOP = ? Correct Answer 55° 

Given:

Two tangents AP and AQ are drawn to a circle with centre O from external point A, where P and Q are points on circle. if ∠ PAQ = 70° 

Concept used:

Tangent to the circle at the radius always makes 90° 

Calculation:

Calculation:

AP and AQ are the two tangents drawn to the circle. ∠ PAQ = 70° 

OA divides the ∠ PAQ in two equal parts so ∠ PAQ = 70/2 = 35° 

in Δ POA ∠ OPA = 90°, ∠ PAQ = 35° 

∠ AOP = 180 - (90+35)

∠ AOP = 180 - 125

∠ AOP = 55° 

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