Question

if two equal chords of a circle intersect within the circle prove that the segments of one chord are equal to corresponding segment of other chord.



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Answer 1

Answer:Given; circle with centre O in which chords AB and CD intersect at M.
To Prove: AM = DM and CM = BM


In ΔAOM and ΔDOM
OA = OD (radii)
OM = OM (common side)
So, ΔAOM ≈ Δ DOM
Hence, AM = DM proved
It is given that AB = CD
So, AB – AM = CD – DM
Or, CM = BM proved