Question

In the given figure, if two chords PQ and RS of a circle with centre O intersect each other at M such that

PM = MS, then prove that MR = MQ.​

Answer 1

Given  :   two chords PQ and RS of a circle with centre O intersect each other at M such that PM = MS

To Find : prove that MR = MQ.​

Solution:

Join PR and SQ

m∠QSR = m∠QPR   Angle by same arc in same arc segment

=> m∠QSM = m∠MPR

Compare  ΔPMR and ΔSMQ  

PM = SM    given  

m∠SMQ = m∠PMR (Vertically opposite angles)

m∠QSM = m∠MPR  

ΔPMR ≅ ΔSMQ  ( ASA)

∴ MR = MQ ( CPCT)

QED

Hence proved

Learn More:

Ab is the diameter of a circle with centre o and cd is chord prove ...

brainly.in/question/8079524

In the adjoining figure, O is the centre of acircle. Chord CD is parallel ...

brainly.in/question/13499168