Prove that

OR

Prove that

Draw a circle of radius 4 cm. From the point 7 cm away from its centre, construct the pair of tangents to the circle.

OR

Draw a line segment of length 8 cm and divide it in the ratio 2:3.

Following figure depicts a park where two opposite sides are parallel and left and right ends are semi-circular in shape. It has a 7m wide track for walking

Two friends Seema and Meena went to the park. Meena said that area of the track is 4066 m². Is she right. Explain.

Prove that 5 - √3 is irrational, given that √3 is irrational.

OR

An army contingent of 616 members is to march behind an army band of 32 members in a parade. The two groups are to march in the same number of columns. What is the maximum number of columns in which they can march?

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