1. State Thales theorem and prove it.

2. AB is a line segment and M is its midpoint. Semicircles are drawn with AM, MB, and AB as diameters on the same side of the line AB. A circle with O as center and r as radius is drawn so that it touches all the three semicricles. Prove that

.

3. Prove that any four vertices of a regular pentagon are concyclic.

4. If

,
show that

.

5. Find X and Y if

and

.

6. Find the Standard Deviation of the following:-

C.I.    0-10     10-20     20-30     30-40
f         3           4            2           5

7. A number is selcted at random from 40 to 80. Find the probability that it is divisible by 6 or 9.

8. Prove the identity:-

.

9. Find the area of an isosceles triangle with base 10 cm and vertical angle 47°.

10. The angle of elevation of a jet plane from a point P on the ground is 60°. After 15 seconds, the angle of elevation changes to 30°. If the jet is flying at the speed of 720 km/hour, find the height at which the jet is flying.