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Quantitative Aptitude

Circles

In the figure...

Question

In the figure given below (not drawn to scale), A,B,C are three points on a circle with center O. The chord BA is extended to a point T such that CT becomes a tangent to the circle at point C. If $∠ A T C = 30^{\circ}$ and $∠ A C T = 50^{\circ}$ . Find $∠ B O A$ .

100^{\circ}

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150^{\circ}

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80^{\circ}

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cannot be determined

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Solution

The correct option is A $100^{\circ}$
The correct answer is option (a). Check the video for the approach.

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Similar questions

Q. In the figure given below (not drawn to scale), A, B and C are three points on a circle with centre O. The chord BA is extended to a point T such that CT becomes a tangent to the circle at point C. If

∠

ATC = 30

^{\circ}

and

∠

ACT = 50

^{\circ}

, then the angle

∠

BOA is :

∠

ATC = 30

^{\circ}

and

∠

ACT = 50

^{\circ}

, then the

∠

BOA is :
(CAT 2003)

A, B & C are three points on a circle. The tangent at C meets BA produced at T. Given that ∠ATC = 36^o & ∠ACT = 48^o, calculate the angle subtended by AB at the center of the circle.

In the given figure, A, B and C are three points on the circle with centre O such that $∠ B O C = 30^{\circ}$ and $∠ A O B = 60^{\circ}$ . If D is a point on the circle that is not on the arc ABC, then find $∠ A D C .$

Q. In the given figure, if TP and TQ are tangents drawn from an external point T to a circle with centre O such that ∠TQP = 60°, then ∠OPQ =

(a) 25°

(b) 30°

(c) 40°

(d) 60°

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In the figure given below (not drawn to scale), A,B,C are three points on a circle with center O. The chord BA is extended to a point T such that CT becomes a tangent to the circle at point C. If ∠ATC=30∘ and ∠ACT=50∘. Find ∠BOA.

The correct option is A 100∘The correct answer is option (a). Check the video for the approach.

In the figure given below (not drawn to scale), A,B,C are three points on a circle with center O. The chord BA is extended to a point T such that CT becomes a tangent to the circle at point C. If $∠ A T C = 30^{\circ}$ and $∠ A C T = 50^{\circ}$ . Find $∠ B O A$ .

The correct option is A $100^{\circ}$
The correct answer is option (a). Check the video for the approach.