# Tangent Perpendicular to Radius at Point of Contact

## Trending Questions

**Q.**Question 6

The length of a tangent from a point A at distance 5 cm from the centre of the circle is 4 cm. Find the radius of the circle.

**Q.**Question 1

From a point Q, the length of the tangent to a circle is 24 cm and the distance of Q from the centre is 25 cm. The radius of the circle is

(A) 7 cm

(B) 12 cm

(C) 15 cm

(D) 24.5 cm

**Q.**

Prove that the perpendicular at the point of contact to the tangent to a circle passes through the centre.

**Q.**

In figure AB is a diameter of a circle with centre O and AT is a tangent. If ∠AOQ=58∘, find ∠ATQ.

**Q.**In the given figure, CD is the tangent at Q and ∠RQD=x∘, then the measure of ∠RPQ is equal to

90∘

(180−x)∘

x∘

(180+x)∘

**Q.**Question 6

Draw a circle of radius 4 cm. Construct a pair of tangents to it, the angle between which is 60∘. Also justify the construction. Measure the distance between the centre of the circle and the point of intersection of tangents.

**Q.**In figure, O is the centre of the circle and BCD is tangent to it at C. Prove that ∠BAC+∠ACD=90∘

**Q.**

A point P is 10 cm away from the center of a circle. The length of the tangent drawn from P to the circle is 8 cm. The radius of the circle is equal to ____.

5 cm

6 cm

4 cm

3 cm

**Q.**

In the given figure, AB and AC are tangents to a circle with centre O and radius 8 cm. If OA = 17 cm, then the length of AC (in cm) is

(a) 9 (b) 15 (c) √353 (d) 25

**Q.**A circle of radius r is inscribed in a triangle of area ′Δ′. If the semi-perimeter of the triangle is s, then the correct relation is

- r=Δs

- r=sΔ

- 2s=Δr
- 2r=Δs

**Q.**

The length of the tangent from a point A to a circle, of radius 3 cm, is 4 cm. Find the distance of A from the center of the circle.

√7 cm

7 cm

5 cm

25 cm

**Q.**

In the given figure, point P is 26 cm away from the centre O of a circle and the length PT of the tangent drawn from P to the circle is 24 cm. Then the radius of the circle is

(a) 10 cm (b) 12 cm (c) 13 cm (d) 15 cm

**Q.**

In the following figure, PQ is a chord of a circle with centre O and PT is a tangent. If ∠ QPT = 60o, find ∠ PRQ.

**Q.**

In figure, PQ is a tangent from an external point P to a circle with centre O and OP cuts the circle at T and QOR is a diameter. If ∠POR=130∘ and S is a point on the circle, find ∠1+∠2

**Q.**

PQ is a tangent to a circle with centre O at the point P. If Δ OPQ is an isosceles triangle, then ∠ OQP is equal to

(a) 30o (b) 45o (c) 60o (d) 90o

**Q.**

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

**Q.**Statement 1: A tangent is perpendicular to the radius at the point of contact.

Statement 2: A line from the centre to any other point on the tangent has a length greater than the radius of the circle.

- Statement 1 is the correct explanation for statement 2.
- Statement 2 is the correct explanation for Statement 1
- Statement 1 and Statement 2 are false.
- Statement 2 is a theorem and Statement 1 is false.

**Q.**

In the given figure, PQ is a tangent to a circle with centre O. A is the point of contact. If ∠ PAB = 67o, then the measure of ∠ AQB is

(a) 73o (b) 64o (c) 53o (d) 44o

**Q.**

In the given figure, O is the centre of a circle, AOC is its diameter such that ∠ ACB = 50o . If AT is the tangent to the circle at the point A then ∠ BAT = ?

(a) 40o (b) 50o (c) 60o (d) 65o

**Q.**

In the given figure, O is the centre of two concentric circles of radii 4 cm and 6 cm respectively. PA and PB are tangents to the outer and inner circle respectively. If PA = 10 cm, find the length of PB up to one place of decimal.

**Q.**

In the given figure, PQ and PR are tangents to a circle with centre A. If ∠ QPA = 27o then ∠ QAR equals

(a) 63o (b) 117o (c) 126o (d) 153o

**Q.**

If PA and PB are two tangents to a circle with centre O such that ∠ AOB = 110o then ∠ APB is equal to

(a) 55o (b) 60o (c) 70o (d) 90o

**Q.**

Equal circles with centres O and O' touch each other at X. OO' produced to meet a circle with centre O', at A. AC is a tangent to the circle whose centre is O. O' D is perpendicular to AC. Find the value of DO′CO

**Q.**

Two concentric circles are of diameters 30cm and 18cm. Find the length of the chord of the larger circle which touches the smaller circle.

**Q.**

PQ is a tangent to a circle with centre O at the point P. If △OPQ is an isosceles triangle such that OP = PQ, then find the measure of ∠OQP.

30∘

45∘

60∘

90∘

**Q.**

In the given figure, O is the centre of the circle. PA and PB are tangents. Show that AOBP is a cyclic quadrilateral.

**Q.**

In the given figure, O is the centre of a circle, PQ is a chord and PT is the tangent at P. If ∠ POQ = 70o, then ∠ TPQ is equal to

(a) 35o (b) 45o (c) 55o (d) 70o

**Q.**

In the given figure, DE and DF are tangents from an external point D to a circle with centre A. If DE = 5 cm and DE ⊥ DF then the radius fo the circle is

(a) 3 cm (b) 4 cm

(c) 5 cm (d) 6 cm

**Q.**Question 9

Prove that the tangent drawn at the mid-point of an arc of a circle is parallel to the chord joining the end points of the arc.

**Q.**

If PA and PB are two tangents to a circle with centre O such that ∠ APB = 80o. Then, ∠ AOP = ?

(a) 40o (b) 50o (c) 60o (d) 70o