AP and BP are tangents to circle with centre O at A and B respectively. If $∠ A P B = 80^{\circ}$ , find $∠ A O B$

90^{\circ}

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100^{\circ}

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120^{\circ}

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150^{\circ}

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Solution

The correct option is B $100^{\circ}$
In $□ A O B P$ ,
$∠ A O B + ∠ A + ∠ B + ∠ A P B = 360^{o}$ ...Angle sum property of quadrialteral
$∠ A O B = 360^{\circ} - 90^{\circ} - 90^{\circ} - 80^{\circ} = 100^{\circ}$

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In the given figure , AC and BC are tangents to the circle with centre O.

If $∠ A C B$ is twice $∠ A O B$ , then $∠ A C B$ = ____

If PA and PB are two tangents to a circle with centre O such that $∠$ AOB = $110^{o}$ then $∠$ APB is equal to

(a) $55^{o}$ (b) $60^{o}$ (c) $70^{o}$ (d) $90^{o}$

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