Q27 of 49 Page 1

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


Given: PT and PS are tangents from an external point P to the circle with center O.


To Prove: PT = PS


Const: Join O to P, T, and S


Proof: In Δ OTP and Δ OSP


OT=OS …[radii of the same circle


OP=OP …[Common


∠ OTP =∠ OSP …[Each 90 �


∠ OTP =∠ OSP …[R.H.S. congruence condition


∴ PT = PS (by CPCT)


More from this chapter

All 49 →
25

A motor boat whose speed is 20 km/h in still water, takes 1 hour more to go 48 km upstream than to return downstream to the same spot. Find the speed of the stream.

Or


Find the roots of the equation

26

If the sum of first 4 terms of an A.P. is 40 and that of first 14 terms is 280, find the sum of its first n terms.

Or


Find the sum of the first 30 positive integers divisible by 6.

 28

In fig. 6, arcs are drawn by taking vertices A, B and C of an equilateral triangle ABC of side 14 cm as centers to intersect the sides BC, CA and AB at their respective mid-points D, E and F. Find the area of the shaded region.

29

From a solid cylinder whose height is 15 cm and diameter 16 cm, a conical cavity of the same height and same diameter is hollowed out. Find the total surface area of the remaining slid.