# Intersection between Tangent and Secant

## Trending Questions

**Q.**The common tangents to the circle x2+y2=2 and the parabola y2=8x touch the circle at the points P & Q and the parabola at the points R & S. Then, the area (in sq units) of quadrilateral PQRS is ?

- 3
- 6
- 9
- 15

**Q.**The pair of tangents AP and AQ drawn from an external point to a circle with centre O are perpendicular to each other and length of each tangent is 5 cm. The radius of the circle is

(a) 10 cm (b) 7.5 cm (c) 5cm (d) 2.5 cm

**Q.**What is the distance between two parallel tangents of a circle of radius 4 cm?

**Q.**

If from any point on the common chord of two intersecting circles, tangents be drawn to the circles, prove that they are equal.

**Q.**In the given figure, O is the centre of a circle and PQ is a diameter. If ∠ROS=40∘, then what is the value of ∠RTS?

- 20∘
- 45∘
- 70∘
- 65∘

**Q.**In the given figure, PT is a tangent to a circle with centre O. If OT = 6 cm and OP = 10 cm, then the length of tangent PT is

(a) 8 cm

(b) 10 cm

(c) 12 cm

(d) 16 cm

**Q.**PQ is a chord of length 16 cm of a circle of radius 10 cm. The tangent at P and Q intersect at a point T as shown in the figure. Find the length of TP [CBSE 2013C]

**Q.**In the given figure, O is the centre of the circle and TP is the tangent to the circle from an external point T. If ∠PBT = 30

^{∘}, prove that

BA : AT = 2 : 1 [CBSE 2015]

**Q.**In the given figure, PA and PB are two tangents from an external point P to a circle with centre O. If ∠PBA = 65

^{∘}, find ∠OAB

^{ }and ∠APB

**Q.**In the given figure, PA and PB are two tangents to a circle with centre O, If ∠APB = 60

^{∘}then find the measure of ∠OAB

**Q.**In Fig. 10.85, PQ is a chord of a circle and PT is the tangent at P such that $\angle $QPT = 60

^{0}. Then , find $\angle $PRQ .

figure

**Q.**

In the given figure, PA is tangent to the circle. If PC intersects the circle at B and PB = 9 cm and BC =7cm, PA =

18 cm

12 cm

16 cm

10 cm

**Q.**

Two tangents to the circle ${x}^{2}+{y}^{2}=4$ at the points $A$and $B$ meet at $P(-4,0).$

The area of the quadrilateral $PAOB$ where $O$ is the origin, is

$4$ sq. units

$6\sqrt{2}$ sq. units

$4\sqrt{3}$ sq. units

None of these

**Q.**

Among the complex number z satisfying condition $|z+1-i|\le 1,$the number having the least positive argument is

$1-i$

$-1+i$

$-i$

None of these

**Q.**In the given figure, two circles touch each other at C and AB is a tangent to both the circles. The measure of ∠ACB is

(a) 45

^{∘}

(b) 60

^{∘}

(c) 90

^{∘}

(d) 120

^{∘ }

**Q.**

AB and BC are the tangents to the circle from the points B. D is the centre of the circle. BD = 5 cm and CD = 3 cm. Find the value of AB - BC.

20 cm

4 cm

0 cm

9 cm

**Q.**If two tangents inclined at an angle of 60

^{0 }are drawn to a circle of radius 3 cm , then length of each tangent is equal to

(a) $\frac{3\sqrt{3}}{2}$ (b) 6 cm (c) 3 cm (d) $3\sqrt{3}$ cm

**Q.**

In quadrilateral ABCD; angle D = 90o, BC = 38 cm and DC = 25 cm. A circle is inscribed in this quadrilateral which touches AB at point Q such that QB = 27 cm. Finthe the radius of the circle.

**Q.**

In the above given figure, PB = 9 cm, CP = 4 cm and TP is a tangent at T. Find PT.

2 cm

6 cm

9 cm

8 cm

**Q.**

AB is a tangent to a circle with centre O and A is the point of contact. If , prove that AB = OA.

**Q.**

In the given figure 'O' is the center of the circle. SP and TP are the two tangents at S and T respectively. ∠SPT is 50∘, the value of ∠SQT is:

125°

65°

115°

None of the above

**Q.**In the given figure, O is the centre of two concentric circles of radii 6 cm and 10 cm. AB is a chord of outer circle which touches the inner circle. The length of AB is

(a) 8 cm

(b) 14 cm

(c) 16 cm

(d) $\sqrt{136}$ cm

**Q.**

In the given figure, 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.**

In the picture below, the radius of the circle is 15 centimetres. Compute the lengths of the tangents PQ and PR

(i) The point P is equidistant from A and B

(ii) The line OP bisects the line AB and the angle APB

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

^{∘}, then the measure of ∠AQB is

(a) 73

^{∘}

(b) 64

^{∘}

(c) 53

^{∘}

(d) 44

^{∘}

**Q.**In the given figure, a circle is inscribed in a quadrilateral ABCD touching its sides Ab, BC, CD and AD at P, Q, R and S respectively.

If the radius of the circle is 10 cm, BC = 38 cm, PB = 27 cm and AD ⊥ CD then the length of CD is [CBSE 2013]

(a) 11 cm

(b) 15 cm

(c) 20 cm

(d) 21 cm

**Q.**If TP and TQ are 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.**

In the circle centred at O, the tangents at A and B intersect at P. Prove the following:

(i)

the point P is equidistant from A and B

(ii)

the line OP bisects the line AB and the angle APB

(iii)

if the line OP cuts the line AB at Q, then OQ × OP = r^{2}, where r is the radius of the circle

**Q.**If from any point on the common chord of two interesting circle, tangents be drawn to the circles, prove that they are equal.

**Q.**In the given figure, O is the centre of a circle PT and PQ are tangents to the circle from an external point P. If ∠TPQ = 70

^{∘}then ∠TRQ

[CBSE 2015]