# Angle between Tangents Drawn from an External Point

## Trending Questions

**Q.**Question 6

In a right angle ∠ ABC is which ∠B=90∘, a circle is drawn with AB as diameter intersecting the hypotenuse AC at P. Prove that the tangent to the circle at P bisects BC.

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

**Q.**If AP and AQ are the two tangents to a circle with centre O so that ∠POQ = 120°, then∠PAQ is equal to ___.

- 70°
- 60°
- 80°
- 90°

**Q.**

In the given figure, XY is a diameter of the circle, PQ is a tangent to the circle at Y. Given that ∠AXB = 500 and ∠ABX = 700, calculate ∠APY.s

**Q.**

PA and PB are the two tangents drawn to the circle. O is the center of the circle. A and B are the points of contact of the tangents PA and PB with the circle. If ∠OPA=35∘, then find ∠POB.

55∘

65∘

75∘

85∘

**Q.**In the given figure, PA and PB are two tangents drawn from an external point P. If ∠APB=40∘, then ∠PAB=

- 70∘
- 90∘
- 60∘

**Q.**

**Question 4**

If AB is a chord of a circle with centre O, AOC is a diameter and tangent T at A as shown in the figure. Prove that ∠BAT = ∠ACB.

**Q.**

**Question 3**

From an external point P, two tangents , PA and PB are drawn to a circle with centre O. At one point E on the circle tangent is drawn which intersects PA and PB at C and D, respectively. If PA = 10 cm, find the perimeter of the triangle PCD.

**Q.**AP and AQ are the two tangents drawn to a circle with centre O, these tangents are inclined to each other at an angle 600. Find ∠APQ in the given figure.

- 80∘
- 70∘
- 60∘
- 90∘

**Q.**

Prove that the tangents drawn at the ends of a chord of a circle make equal angles with the chord.

**Q.**Question 6

In figure, AT is a tangent to the circle with centre O such that OT = 4 cm and ∠OTA=30∘ . Then , AT is equal to

(A) 4 cm

(B) 2 cm

(C) 2 √3 cm

(D) 4 √3 cm

**Q.**In the given figure, AP and AQ are the tangents drawn to a circle from a point A outside the circle. If ∠PAQ = 40∘ then, find ∠AQP.

- 90∘
- 35∘
- 70∘
- 20∘

**Q.**In the given figure, O is the centre of the circumcircle. Tangents at A and C intersect at P. Given ∠ AOB=140∘ and ∠APC = 80∘; find the ∠ BAC.

- 90∘
- 20∘
- 60∘
- 50∘

**Q.**

**Question 6**

In a right angle ∠ ABC is which ∠B=90∘, a circle is drawn with AB as diameter intersecting the hypotenuse AC at P. Prove that the tangent to the circle at P bisects BC.

**Q.**

**Question 7**

In figure, tangents PQ and PR are drawn to a circle such that ∠RPQ=30∘. A chord RS is drawn parallel to the tangent PQ. Find the ∠ RQS.

**Q.**

Two tangents PA and PB are drawn to a circle with center O from an external point P. Prove that ∠APB=2∠OAB [3 MARKS]

**Q.**

**Question 12**

The tangent at a point C of a circle and a diameter AB when extended intersect at P. If ∠PCA=110∘ , find ∠ CBA.

**Q.**In the given figure, AP and AQ are the tangents drawn to a circle from a point A outside the circle. If ∠PQA= 65∘ then, find ∠PAQ.

- 100∘
- 25∘
- 90∘
- 50∘

**Q.**

**Question 4**

If from an external point B of a circle with centre O, two tangents BC and BD are drawn such that ∠ DBC = 120∘, prove that BC+BD=BO i.e BO = 2BC.

**Q.**If TP and TQ are two tangents to a circle with centre O so that ∠POQ=110o, then ∠PTQ is equal to

- 60o
- 80o
- 70o
- 90o

**Q.**In the given figure, PA and PB are two tangents drawn from an external point P. If ∠APB=40∘, then ∠AOB=

( 2 marks)

**Q.**

**Question 4**

If from an external point B of a circle with centre O, two tangents BC and BD are drawn such that ∠ DBC = 120∘, prove that BC+BD=BO i.e BO = 2BC.

**Q.**

- True
- False

**Q.**

Two tangents PA and PB are drawn from an external point P to the circle with centre O, such that ∠APB =120∘what is the relation between OP and AP?

OP = 12 AP

AP = 23 OP

OP = 2 AP

OP = AP

**Q.**In figure, the chord AB of the larger of the two concentric circles, with centre O, touches the smaller circle at C. Prove that AC=CB.

**Q.**

**Question 12**

The tangent at a point C of a circle and a diameter AB when extended intersect at P. If ∠PCA=110∘ , find ∠ CBA.

**Q.**Draw a circle with the help of a bangle. Take a point P outside the circle. Construct the pair of tangents from this point P to the circle.

**Q.**In the given figure PQ and PR are two tangents on a circle with centre O. If ∠QPR=60∘, then ∠QRO=30∘.

- True
- False

**Q.**Question 6

In figure, AT is a tangent to the circle with centre O such that OT = 4 cm and ∠OTA=30∘ . Then , AT is equal to

(A) 4 cm

(B) 2 cm

(C) 2 √3 cm

(D) 4 √3 cm

**Q.**In the given figure, PA and PC are the tangents. Find the value of the angle APC.

- 90 degrees
- 30 degrees
- 50 degrees
- 60 degrees