CBSE Class 10 Maths (Basic) 2024 · Paper 430(B) · Question 30

Circles 3 marks Very hard

Two tangents

P A

and

P B

are drawn to a circle with centre

O

from an external point

P

. Prove that

∠ A P B = 2 ∠ O A B

Answer

Since

P A = P B

∠ P A B = 9 0^{\circ} - \frac{1}{2} ∠ A P B

; since

∠ O A P = 9 0^{\circ}

∠ O A B = 9 0^{\circ} - ∠ P A B = \frac{1}{2} ∠ A P B

. Hence proved:

∠ A P B = 2 ∠ O A B

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