Circles

Q. In the given figure, there are two circles with the centres O and O' touching each other internally at P. Tangents TQ and TP are drawn to the larger circle and tangents TP and TR are drawn to the smaller circle. Find TQ : TR.

1. 8 : 7
2. 7 : 8
3. 5 : 4
4. 1 : 1

Q. Three circles touch each other externally. The distance between their centre is 5 cm, 6 cm and 7 cm. Find the radii of the circles:

1. 2 cm, 3 cm, 4 cm
2. 3 cm, 4 cm, 1 cm
3. 1 cm, 2.5 cm, 3.5 cm
4. 1 cm, 2 cm, 4 cm

Q. In the given figure, 'O' is the centre of the circle. SP and TP are the two tangents at S and T respectively. $\angle SPT$ is ${50}^{\circ }$, the value of $\angle SQT$ is

1. none of the above
2. ${125}^{\circ }$
3. ${65}^{\circ }$
4. ${115}^{\circ }$

Q. In the adjoining figure, BD is the diameter of the circle and $\angle BCA={41}^{\circ }.Find\angle ABD$.

1. ${41}^{\circ }$
2. ${49}^{\circ }$
3. ${22.5}^{\circ }$
4. ${20.5}^{\circ }$

Q. In the figure below, X is a point on diameter AB of the circle with centre O, such that AX = 9 cm, XB = 5 cm. Find the radius of the circle (centre Y) which touches the diameter at X and touches the circle, centre O, internally at Z.

1. $3\frac{1}{14}cm$
2. $3\frac{3}{14}cm$
3. $2\frac{1}{14}cm$
4. $2\frac{3}{14}cm$

Q. In the adjoining figure, 'O' is the centre of the circle and PQ , PR and ST are the three tangents. $\angle QPR={50}^{\circ }$, then the value of $\angle SOT$ is

1. can't be determined
2. ${30}^{\circ }$
3. ${75}^{\circ }$
4. ${65}^{\circ }$

Q. ABC is a right angled triangle, AB = 3cm, BC = 5 cm and AC = 4cm, then the inradius of the circle is:

1. 1 cm
2. 1.25 cm
3. 1.5 cm
4. None of these

Q. O and O' are the centres of circle of radii 20 cm and 37 cm. AB = 24 cm. What is the distance OO'?

1. 51 cm
2. 48 cm
3. 45 cm
4. 35 cm

Q. In the adjoining figure, 2 circles with centres Y and Z touch each other externally at point A.

Another circle, with centre X, touches the other 2 circles internally at B and C. If XY = 6 cm, YZ = 9 cm and ZX = 7 cm, then find the radius of the circle with centre Y.

1. 13
2. 5
3. 8
4. 17

Q. In the adjoining figure, ABCD is a rectangle in which length is twice of breadth. H and G divide the line CD into three equal parts. Similarly points E and F trisect the line AB. A circle PQRS is circumscribed by a square PQRS which passes through the points E, F, G and H. What is the ratio of areas of circle to that of rectangle?

1. 25$\pi$ : 72
2. $3\pi :7$
3. 3 : 4
4. 32 $\pi$ : 115