A tangent from a point P outside the circle meets the circle at M. Then $∠ M O P =$ , if $∠ M P O = 30^{\circ}$ .

30^{\circ}

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60^{\circ}

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45^{\circ}

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Solution

The correct option is B $60^{\circ}$
Angle between MP and OM is $90^{\circ}$ and $∠ M P O = 30^{\circ} .$

$∴ ∠ M O P = 180^{\circ} - (90^{\circ} + 30^{\circ}) = 60^{\circ}$

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Similar questions

Q. In the given figure, O is the centre of a circle. BOA is its diameter and the tangent at the point P meets BA extended at T. If ∠PBO = 30°, then ∠PTA = ?

(a) 60°
(b) 30°
(c) 15°
(d) 45°

Q. In Fig. 10.87 , BOA is a diameter of a circle and the tangent at a point P meets BA produced at T . If

∠

PBO = 30⁰ , then find

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figure

Q. A tangent from a point P outside the circle meets the circle at M. Then

∠ M O P =

, if

∠ M P O = 30^{\circ}

Q. A tangent from a point P outside the circle meets the circle at M. Then

∠ M O P =

, if

∠ M P O = 30^{\circ}

Tangents from a point P are drawn onto a circle with angle between them as $120^{\circ}$ . The tangents from P meet the circle at A and B. If a line is drawn from point P through the center of the circle O, then find the measure of $∠$ POA.

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A tangent from a point P outside the circle meets the circle at M. Then ∠MOP= , if ∠MPO=30∘.

The correct option is B 60∘Angle between MP and OM is 90∘ and ∠MPO=30∘. ∴∠MOP=180∘−(90∘+30∘)=60∘

A tangent from a point P outside the circle meets the circle at M. Then $∠ M O P =$ , if $∠ M P O = 30^{\circ}$ .

The correct option is B $60^{\circ}$
Angle between MP and OM is $90^{\circ}$ and $∠ M P O = 30^{\circ} .$

$∴ ∠ M O P = 180^{\circ} - (90^{\circ} + 30^{\circ}) = 60^{\circ}$