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If tangents PA and PB from a point P to a circle with centre O

Question

If tangents $P A$ and $PB$ from a point $P$ to a circle with centre $O$ are inclined to each other at angle of $8 0^{o}$ , then $∠ PO A$ is equal to.

5 0^{o}

6 0^{o}

7 0^{o}

8 0^{o}

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Levi Discussed

If tangents

P A

and

PB

from a point

P

to a circle with centre

O

are inclined to each other at angle of

8 0^{o}

, then

∠ PO A

is equal to.

12 mins ago

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12 mins ago

Text solutionVerified

Given:

∠ A PB = 8 0^{\circ}

As we know that sum of

∠ A PB + ∠ A OB = 18 0^{\circ}

(Using Property)

∠ A OB = 10 0^{\circ}

Δ

A OP

≃

Δ

BOP

by SSS congruency criteria.

A O = BO

(Radius of circle)

PO = PO

(common side of triangle)

A P = BP

(tangents form an external point)

∠ A OP = ∠ BOP

(CPCT )

∠ PO A + ∠ POB = ∠ A OB = 10 0^{\circ}

∠ PO A = 5 0^{\circ}

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Question Text	If tangents $P A$ and $PB$ from a point $P$ to a circle with centre $O$ are inclined to each other at angle of $8 0^{o}$ , then $∠ PO A$ is equal to.
Answer Type	Text solution:1
Upvotes	150