# Tangents Drawn from an External Point

## Trending Questions

**Q.**

A triangle ABC is drawn to circumscribe a circle of radius 4 cm such that the tangents BD and DC into which BC is divided by the point of contact D are of lengths 8 cm and 6 cm respectively. Find the sides AB and AC.

**Q.**The maximum number of tangents that can be drawn to a circle from an external point is

**Q.**What the distance between two parallel tangents to a circle of radius 5 cm?

**Q.**

A circle is inscribed in a triangle with sides 3, 4 and 5 cm. The radius of the circle is

**Q.**Two circles touch each other externally at P. AB is a common tangent to the circle touching them at A and B. The value of $\angle $APB is

(a) 30º (b) 45º (c) 60º (d) 90º [CBSE 2014]

**Q.**Consider the following statements and choose the correct option.

1) A tangent is a line that touches the circle at one point.

2) A tangent is a special case of the secant where the points of intersection coincide.

- 1 is false and 2 is true
- Both 1 and 2 are true
- Both 1 and 2 are false
- 1 is true and 2 is false

**Q.**Two tangents PA and PB are drawn from an external point P to a circle with centre O. Prove that AOBP is a cyclic quadrilateral.

**Q.**

In the given figure, TAS is a tangent to the circle, with centre O, at the point A. If ∠OBA = 32∘, find the value of x.

**Q.**What is the distance between two parallel tangents of a circle having radius 4.5 cm ? Justify your answer.

**Q.**

In the figure given below, AC is a transverse common tangent to two circles with centres P and Q and of radii 6 cm and 3 cm respectively.

Given that AB = 8 cm, calculate PQ.

16 cm

15 cm

19 cm

25 cm

**Q.**In Fig. 3, two tangents PQ are PR are drawn to a circle with centre O from an external point P. Prove that ∠QPR = 2 ∠OQR.

**Q.**Two tangents making an angle of 120° with each other are drawn to a circle of radius 6 cm, then the length of each tangent is equal to

(a) $\sqrt{3}cm$

(b) 6 $\sqrt{3}cm$

(c) $\sqrt{2}cm$

(d) 2 $\sqrt{3}cm$

**Q.**If PT is a tangent at T to a circle whose centre is O and OP = 17 cm, OT = 8 cm, Find the length of the tangent segment PT.

**Q.**

In the given fig., angle OBC = 30^{o}, then value of x is:

15

^{o}110

^{o}100

^{o}30

^{o}

**Q.**

In the given figure, AB is the diameter of a circle and P is a point on AB extended.

A tangent from P touches the circle at Q. If PQ = 4 cm and PA = 8 cm ,

then the radius of the circle is ____ cm.

3.5 cm

4 cm

3 cm

2 cm

**Q.**

In the following figure, a circle is inscribed in the quadrilateral ABCD. If BC = 38 cm. QB = 27 cm, DC = 25 cm and that AD is perpendicular to DC, find the radius of the circle.

34 cm

24 cm

13 cm

14 cm

**Q.**

In the figure, PM is a tangent to the circle and PA = AM. Find PA.PB = ?

MB

^{2}1.5 MB

2 MB

MB

1.75 MB

**Q.**What is the value of angle QPR in degrees?

- 30
- 60
- 120
- 20

**Q.**In an isosceles triangle ABC, AB = BC, ∠B = 20◦. M, N are on AB and BC respectively such that ∠MCA = 60◦, ∠NAC = 50◦. Find ∠NMC in degrees.

**Q.**Theorem: Tangent segments drawn from an external point to a circle are congruent

**Q.**In the given figure, seg EF is a diameter and seg DF is a tangent segment. The radius of the circle is

*r.*Prove that, DE × GE = 4

*r*

^{2}

**Q.**In Fig . 10.69, the tangent at a point C of a circle and a diameter AB when extended intersect at P . If $\angle $PCA =110

^{0}, find $\angle $CBA. [Hint: Join CO.]

figure

**Q.**

The length of the tangent to the circle from an exterior point P is 5cm. What is the length of another tangent drawn to the same circle from the exterior point P?

**Q.**

From an external point P, two tangents are drawn that touch the circle at points Q and R. The centre of the circle is O. Points O and P are joined. The ratio of angles OPR and OPQ is

1:1

2:1

3:1

4:1

**Q.**To draw a pair of tangents to a circle which are inclined to each other at an angle of 45∘, it is required to draw tangents at end points of those two radii of the circle, the angle between them should be

- 135
- 60
- 90
- 45

**Q.**

Prove that the least perimeter of an isosceles triangle in which a circle of radius $r$ can be inscribed is $6\sqrt{3r}$.

**Q.**The maximum number of tangents that can be drawn from an external point to a circle is:

- 1
- 2
- 3
- 4

**Q.**PQ and PR are two tangents drawn from a point P. If centre 'O' of the circle and P are joined, then

∠OPR:∠OPQ =

- 2:1
- 1:1
- 1:2
- 4:1

**Q.**In the given figure, AP and AQ are the tangents drawn to a circle from a point A outside the circle.

If ∠PAQ = 50∘ then, find ∠OPQ.

- 100∘
- 50∘
- 25∘
- 12.5∘

**Q.**In the figure given below, PA and PB are tangents to the circle from point P. Which of the following is the correct relation between PA and PB?

- PA>PB
- PA=PB
- PA<PB
- PA2=PB2+r2