In the given, AB and CD are equal chords of a circle with centre O and OP⊥ AB, OQ⊥AC

Prove that PB = QC 

Asked by pereiracalida | 14th Jan, 2018, 06:55: PM

Expert Answer:

begin mathsize 16px style OP perpendicular AB
rightwards double arrow AL equals LB space space space space left parenthesis Perpendicular space from space centre space bisects space the space chord right parenthesis
Similarly space AM equals MC
But space AB equals AC
rightwards double arrow AB over 2 equals AC over 2
rightwards double arrow LB equals MC
Now comma space OP equals OQ space space space left parenthesis radii space of space same space circle right parenthesis
And comma space OL equals OM space space space left parenthesis equal space chords space areequidistant space from space centre right parenthesis
Now comma space OP minus OL equals OQ minus OM
rightwards double arrow LP equals MQ
In space triangles space LPB thin space and space MQC
LB equals MC
LP equals MQ
angle PLB equals angle QMC equals 90 degree
rightwards double arrow triangle LPB approximately equal to triangle MQC space space space left parenthesis SAS space congruence right parenthesis
rightwards double arrow PB equals QC end style

Answered by Rashmi Khot | 16th Jan, 2018, 10:20: AM