# Tangents through a Point

## Trending Questions

**Q.**

A line which intersects a circle at 2 distinct points is called a

Secant

Chord

No Term

Tangent

**Q.**Question 162

Find the values of x and y in the following kite.

**Q.**

The tangent at any point of a circle and the radius through this point are perpendicular to each other.

False

True

**Q.**

Number of tangents, that can be drawn to a circle, parallel to a given chord is

Zero

2

3

Infinite

**Q.**Question 1

If Radii of two concentric circles are 4 cm and 5 cm, then length of each chord of one circle which is tangent to the other circle, is

(A) 3 cm

(B) 6 cm

(C) 9 cm

(D) 1 cm

**Q.**In Fig. 7, two equal circles, with centres O and O', touch each other at X. OO' produced meets the circle with centre O' at A. AC is tangent to the circle with centre O, at the point C. O'D is perpendicular AC.

Find the value of DO′CO.

**Q.**Question 48

PQRS is a trapezium in which PQ∥SR and ∠P=130∘, ∠Q=110∘. Then, ∠R is equal to

a) 70∘

b) 50∘

c) 65∘

d) 55∘

**Q.**

**Question 2**

In Fig. 10.11, if TP and TQ are the two tangents to a circle with centre O so that ∠POQ=110∘, then ∠PTQ is equal to

(A) 60∘

(B) 70∘

(C) 80∘

(D) 90∘

**Q.**Prove that the lengths of the tangents drawn from an external point to a circle are equal.

**Q.**

Which of the following is/are the types of common tangents?

Drawn at the point of intersection.

Direct common tangent

Transverse common tangent

Parallel to the chord

**Q.**

The chord that touches a circle at exactly one point is called _____.

- secant
- tangent
- diameter
- segment

**Q.**

For an incircle of a triangle, the sides of the triangle are

chords

segment of circle

tangent of a circle

diameter of circle

**Q.**

TA and TB are tangents to a circle with centre O from an external point T. OT intersects the circle at point P. Then prove that AP bisects ∠TAB.

**Q.**What is the maximum number of tangents that can be drawn on a circle from a point outside the circle?

- 1
- 0
- 4
- 2

**Q.**The maximum number of tangents that can be drawn to a circle from a point outside it is ______

(A) 2

(B) 1

(C) one and only one

(D) 0

**Q.**

How many tangents can be drawn at any point on the circle?

1

0

3

2

**Q.**The maximum number of tangents that can be drawn at a point on the circle is:

- 1
- 2
- 3
- 4

**Q.**

**Question 3**

If tangents PA and PB from a point P to a circle with centre O are inclined to each other at an angle of 80∘, then ∠POA is equal to

(A) 50∘

(B) 60∘

(C) 70∘

(D) 80∘

**Q.**Prove that the intercept of a tangent between two parallel tangents to a circle subtends a right angle at a center.

**Q.**AP is the tangent to the circle with centre O and radius 8 cm . If AB = 9 cm, then find the length of tangent AP.

**Q.**

In the given figure △ABC is isosceles with AB = AC and is inscribed in a circle. If DAE is a tangent to the circle, then which of the following statement is true?

DE // BC

△ABC is equilateral

DE intersects BC

None of these

**Q.**

In the given figure, find a+b+c+d.

180∘

360∘

100∘

210∘

**Q.**

In the given figure, there are two concentric circles with center O such that AP is tangent to the bigger circle and AB is tangent to the smaller circle. If ∠APB=∠ABP=30∘, OA=3 cm and OP = 5 cm, then, radius of the smaller circle is

5 cm

√5 cm

6 cm

√6 cm

**Q.**In the given figure, there are two concentric circles with center O such that AP is tangent to the bigger circle and AB is tangent to the smaller circle. If ∠APB=∠ABP=30∘, OA=3 cm and OP =5 cm, then, radius of the smaller circle is

- √6cm
- 5 cm
- √5cm
- 6 cm

**Q.**Two circles of radii 5 cm and 3 cm are concentric. Calculate the length of a chord of the outer circle which touches the inner circle.

- 6 cm
- 9 cm
- 8 cm

4 cm

**Q.**

Tangents from a point P are drawn onto a circle with angle between them as 120∘ . 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.

25∘

30∘

45∘

90∘

**Q.**The maximum number of tangents that can be drawn at a point on the circle is:

- 1
- 3
- 4
- 2

**Q.**From the given figure, find∠AOB(in degrees ). [2 Marks]

**Q.**In the given figure, O is the centre of a circle of radius 5 cm, T is a point such that OT= 13 cm and OT intersects the circle at E. If AB is the tangent to the circle at E, find the length of AB.

**Q.**In the given figure, a circle touches the side BC of ΔABC at P. AB and AC are two tangents drawn from a point A outside the circle. If AQ = 15 cm, find the perimeter of ΔABC.