PA AND PB ARE ARE TWO TANGENTS DRAWN FROM AN EXTERNAL POINT TO A CIRCLE WITH CENTRE O [ALPHABET].. PROVE THAT OP IS THE RIGHT BISECTOR OF LINE SEGMENT AB 
 
 
 
 

Asked by Anirudh | 27th Nov, 2017, 06:22: PM

Expert Answer:

begin mathsize 16px style Let space OP space intersects space AB space at space point space straight C.
In space triangle PAC space and space triangle PBC comma
PA equals PB space space left parenthesis Tangents space from space an space external space point space are space equal right parenthesis
angle APC equals angle BPC space space space space left parenthesis PA space and space PB space are space equally space inclined space to space OP right parenthesis
PC equals PC space space left parenthesis common right parenthesis
rightwards double arrow triangle PAC space approximately equal to triangle PBC space left parenthesis SAS space criterion right parenthesis
rightwards double arrow AC equals BC space and space angle ACP equals angle BCP
But comma space angle ACP plus angle BCP equals 180 degree
rightwards double arrow angle ACP equals angle BCP equals 90 degree
rightwards double arrow OP perpendicular AB end style

Answered by Rashmi Khot | 27th Nov, 2017, 08:24: PM