Prove that tangents from extremities of any chord makes equal angle with the chord.

If the angle between two tangents drawn from a point outside of a circle is 120° . The angle at the centre is

Prove that the sum of n A.M.'s between any two numbers is equal to n times the A.M. of the two numbers.

Prove that the length of tangents drawn from an external point to a circle are equal.

Prove that the ratio of the areas of two similar triangles is equal to the ratio of the squares of the bisectors of the corresponding angles of the triangles. [The end-points of the angular bisectors are on the opposite sides of the angles.]

A tree of 15 m height was broken due to a heavy wind at a height of h m from the ground.But the broken ends were not completely separated and the top of the tree remained just touching the ground in a slanting position.If the broken portion of the tree makes an angle of 30^@ with the ground find h.

Prove that the angle between the two tangents drawn from an external point to a circle is supplementary to the angle subtended by the line-segment joining the points of contact at the centre.

Prove that the area of the equilateral triangle drawn on the hypotenuse of a right angle triangle is equal to the sum of the areas of the equilateral triangles drawn on the other two sides.

A ladder is kept standing at a slanting position against a wall of a house and in this position the base of the ladder is at a distance of 9.5m from the wall.If the ladder makes an angle of 60^@ with the ground level,find the length of the ladder.