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In figure, PA and PB are tangents to the circle with centre O

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In figure, PA and PB are tangents to the circle with centre O such that $∠ A PB = 5 0^{\circ}$ Write the measure of $∠ O A B$

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In figure, PA and PB are tangents to the circle with centre O such that

∠ A PB = 5 0^{\circ}

Write the measure of

∠ O A B

14 mins ago

Discuss this question LIVE

14 mins ago

Text solutionVerified

Given PA & PB are tangent to the circle with center O.

P A = PB

[length of tangent from external point to circle are equal]

Δ P A B

P A = PB

∠ PB A = ∠ P A B

[isosceles triangle]

now

∠ P A B + ∠ PB A + ∠ A PB = 18 0^{o}

[Angle sum prop]

2∠ P A B = 180 - 50 = 130

∠ PB A = ∠ P A B = 6 5^{o}

………..

(1)

Now PA is tangent & OA is radius at point A.

∠ O A P = 9 0^{o}

[tangent at any point is

⊥

to radius]

∠ O A B = ∠ O A P - ∠ P A B = 90 - 65 = 2 5^{o}

Hence angle OAB is

2 5^{o}

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Question Text	In figure, PA and PB are tangents to the circle with centre O such that $∠ A PB = 5 0^{\circ}$ Write the measure of $∠ O A B$
Answer Type	Text solution:1
Upvotes	150