pq and rq are chords of circle equidistant from centre. prove that, the diameter passing through q bisects

Question

pq and rq are chords of circle equidistant from centre. prove that, the diameter passing through q bisects <pqr and <psr

bhumi273 · Answer

@ganeshie8  @perl

ganeshie8 · Answer

picture ?

bhumi273 · Answer

yaa. just a sec...

bhumi273 · Answer

yaa dis is it
can u plzz help me through dis thingy...

bhumi273 · Answer

|dw:1421311341993:dw|

ganeshie8 · Answer

are you trying a two column proof ?

bhumi273 · Answer

nope

bhumi273 · Answer

ok.... but wht is leg hypotanuse

ganeshie8 · Answer

PQ is congruent to QR because chords equidistant from center are congruent.
angles QRS and QPS are 90 degrees as they are semi circle angles and thus they are congruent. segment QS is congruent to itself by reflexive property.

that makes triangles QRS and QPS congruent by Leg-Hypotenuse theorem.

by CPCTC, we have : 
angle QSR = angle QSP  
angle RQS = angnle PQS

So QS is the angle bisector for angles PQR and PSR as desired.

ganeshie8 · Answer

arent you familiar with triagnle congruence theorems like SSS, SAS, AAS, Leg-Hypotenuse ?

ganeshie8 · Answer

http://www.msdgeometry.com/joomla/images/stories/hypotenuse%20leg%20congruence%20theorem.jpg