how can we prove tht two tangents drawn from a single point are equal ????

Asked by Nancy | 29th Jan, 2017, 06:28: PM

Expert Answer:

begin mathsize 16px style Let space straight P space be space the space point space from space which space we space draw space tangents space PA space and space PB.
Let space straight O space be space the space centre space of space the space circle. space space
In space increment OAP space and space increment OBP comma space space
OP equals space OP...... left parenthesis common space side right parenthesis space space
OA equals OB....... left parenthesis radii space of space the space circle right parenthesis space
angle PAO equals space angle PBO space..... left parenthesis tangent space and space radius space are space perpendicular space to space each space other space at space the space point space of space contact right parenthesis space space
Thus comma increment OAP space approximately equal to space increment OBP.... left parenthesis By space RHS space congruency space criterion right parenthesis space
rightwards double arrow PA equals PB space...... left parenthesis cpct right parenthesis
Hence space proved. end style

Answered by Rebecca Fernandes | 29th Jan, 2017, 07:26: PM