Tangent to a Circle

IMPORTANT

Tangent to a Circle: Overview

This Topic covers sub-topics such as Tangent to a Circle, Parallel Tangents to a Circle, Point of Contact of a Tangent to a Circle and, Property Related to Tangent and Radius of a Circle

Important Questions on Tangent to a Circle

HARD
IMPORTANT

In Fig., from an external point P, two tangents PT and PS are drawn to a circle with centre O and radius r. If OP=2r, show thatOTS =OST=30°.

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HARD
IMPORTANT

In the given figure, O is centre of the circle. The radius of the circle is 3.1 cm and PA is tangent drawn to the circle from point P. If OP=x cm and AP=6.2 cm, then find the value of x

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HARD
IMPORTANT

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In the above figure, seg AB and seg AD are tangent segments drawn to a circle with centre C from exterior point A, then prove that

A=12marc BYD-marc BXD

EASY
IMPORTANT

In figure, the radius is 5 cm. OPTQ is a square, find the length of OT.

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HARD
IMPORTANT

If AP=12 cm, OP=13 cm, then CD=?

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MEDIUM
IMPORTANT

The line m is a tangent to the circle C at the point 9, 12. The circle is centred at the origin.

Check if the line m passes through the point 15, 0.

MEDIUM
IMPORTANT

Shown below is a circle and a square. The circle with centre O has a radius of 4 cm.

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Find the area of the shaded region. Show your work and give valid reasons. (Note: If needed, take π as 3.14)

MEDIUM
IMPORTANT

In the figure below, M and N are the centres of two semi-circles having radii 9 cm and 16 cm respectively. ST is a common tangent.

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Find the length of PQ. Draw a rough figure, show your work and give valid reasons.

MEDIUM
IMPORTANT

Shown below is a circle with centre O. NQ is a tangent to the circle.

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Find the measure of OQN. Show your work and give valid reasons.

MEDIUM
IMPORTANT

In the given figure find the value of x if the length of PT=215 cm. Given that the radius of inner and the outer circle are x cm and 2x cm respectively and PQ=23x cm. 

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MEDIUM
IMPORTANT

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Given that, BAY= 30°. Find AQB

MEDIUM
IMPORTANT

In the figure given below, AB is a tangent to the circle with centre O. 

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EASY
IMPORTANT

The radii of two concentric circles are 3.9 cm and 6.5 cm. If a chord of a larger circle touches the smaller circle then the length of the chord is _______cm

MEDIUM
IMPORTANT

In the adjoining fig PA and PB are tangents drawn from an external point P to a circle with centre O. Then prove that AOB+APB=180°

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HARD
IMPORTANT

In the given figure, O is the centre of the circle, MN is tangent to the circle at A. If MAB=60°. Find ABN and ANB.

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MEDIUM
IMPORTANT

In the given figure, AD is a diameter of a circle with centre O and AB is a tangent at AC is a point on the circle such that DC produced intersects the tangent at B and ABC=50°. Find AOC.

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MEDIUM
IMPORTANT

In the given figure, PT is a tangent and PAB is a secant. If PT=6 cm and AB=5 cm, then find the length of PA.

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MEDIUM
IMPORTANT

In the given figure, PQ and PR are tangents to the circle centre O, at P and R, respectively,

Find the value of x.

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HARD
IMPORTANT

The diagram shows a circle , centre O. The line PS is a tangent to the circle. Calculate angle PQS.

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EASY
IMPORTANT

In a park, four poles are standing at positions A, B, C and D around the fountain such that the cloth joining the poles AB, BC. CD and DA touches the fountain at P, Q, R and S respectively as shown in figure:

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Based on the above information, answer the following question:

If O is the centre of the circular fountain, then OSA=