Intersection between Tangent and Secant

Q.

In the figure given below, AR is a tangent to the circle. AM is the secant. Find the length of PM, if AR = 6 cm and AP = 2 cm.

$\left[2Marks\right]$

Q.

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

1. 2 cm

2. 6 cm

3. 9 cm

4. 8 cm

Q.

In the figure given below, AR is a tangent to the circle. AM is the secant. Find the length of PM, if AR = 6 cm and AP = 2 cm.

1. 16 cm

2. 9 cm

3. 8 cm

4. 4 cm

Q.

In the figure given below, PAB is a secant and PR is a tangent to the circle. If PA : AB = 1 : 8, and PR = 15 cm, find the length of PB.

1. 10 cm

2. 20 cm

3. 45 cm

4. 90 cm

Q.

$△ABC$ is isosceles with AB = AC. If a circle through B touches the side AC at its mid-point D and intersects the side AB at P, then $\frac{AP}{AB}$ = ______.

1. $\frac{1}{3}$

2. $\frac{4}{1}$

3. $\frac{1}{4}$

4. $\frac{3}{4}$

Q.

In the given figure, PT touches a circle whose centre is O at R. Diameter SQ produced meets PT at P. If $\angle SPR=x^{\circ }$ and $\angle QRP=y^{circ}$, then which of the following statements relate x and y?

1. $x+2y={90}^{\circ }$
   

2. $x+y={90}^{\circ }$
   

3. $x+2y={45}^{\circ }$
   

4. x=2y

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 = ______ cm.

1. 18 cm

2. 12 cm

3. 16 cm

4. 10 cm

Q.

In the given figure O is the centre of the circle and AB is a tangent at B. If AB = 15 cm and AC =7.5 cm, find the radius of the circle.

1. 22.5 cm

2. 12.5 cm

3. 11.25 cm

4. 11 cm

Q.

In the given figure, AB is a diameter and AC is a chord of the circle and the tangent at C intersects AB produced in D. If $\angle BAC={30}^{\circ }$, then $\angle ACD=$ ______.

1. ${60}^{\circ }$

2. ${30}^{\circ }$

3. ${100}^{\circ }$

4. ${120}^{\circ }$

Q.

In the given figure chord AB extended meets tangent DC at C. If AB = 7cm and BC =9 cm and area of $△CBD=18c{m}^2$,

then area of $△CAD=$ ______

1. $16c{m}^2$
   

2. $24c{m}^2$
   

3. $32c{m}^2$
   

4. $64c{m}^2$