Page 4 - Lesson note-2 Angle subtended by Chord,Ch.- 10 Circle
P. 4
Given: AB is a chord such that AM=BM
To Prove: OM ┴ AB
Construction: Join OA and OB
Proof: In ΔOAM and ΔOBM,
OA = OB [radii of same circle]
OM=OM [Common]
AM=BM [Given]
ΔOAM ≅ ΔOBM [SSS]
∠ OMA =∠OMB [C. P. C. T]
0
∠ OMA +∠OMB =180 (Linear pair)
0
∠ OMA +∠OMA =180
0
2∠ OMA=180
0
∠ OMA=90
0
∠ OMA =∠OMB= 90
OM ┴ AB
Hence Proved.
EX .1 Prove that equal chords of congruent circles subtend equal angles at their centers.
