# Circles Finale (almost)

## Volume 4

## Practice Questions:

1. Two circles touch each other externally at Y. PYQ and RYS are two straight lines intersecting the first circle at P and R and the second circle at Q and S. If SY = 16 units, PY = 8 units, RY = 5 units, find QY.

2. Two circles touch each other internally at Y, YAB and YCD are two straight lines intersecting the larger circle at B and D and the smaller circle at A and C. If CD = 8 units, AB = 7units, YA = 5 units, find the lengths of YD and YC.

3. In the diagram given below, AB is a tangent to the circle and ACD is a secant. BP is the angle bisector of angle CBD meeting CD at P. If angle DAB is 20 degrees and angle CDB is 50 degrees, find the measure of angles angle CPB, angle ABC.

4. Three unequal circles are drawn such that each of those circles touch the other two externally. If the sides of triangle formed by joining the centres of three circles is given as 8 cm, 4 cm and 6 cm. Find the radii of the three circles.

5. In the diagram given below, PT is a tangent to the circle at D. If angle BDC = 30 degrees and angle CDT is 70 degrees, find the measure of angle BCD.

6. Two circles intersect and the length of common chord is 24 units. If their centers are 20 cm apart and radius of one of circle is 15 units, find the area (approximate) of the second circle.

7. Two circles of equal radii intersect each other. If their centers are 32 cm apart and the length of the common chord is 16 cm, find their radius.

8. Two circles having radii 16 and 30 units intersect orthogonally. If the distance between their centers is 34 units, find the length of the common chord.