Question

In following fig. ABC is an equilateral triangle . A circle is drawn with centre A so that ot cuts AB and AC at M and N respectively. Prove that BN = CM.

Answer 1

ABC is an equilateral triangle, 

∴ AB = AC 

Also AN = MB (radii of same circle)

⇒ NC = MB 

In Δ BNC and Δ CMB

NC = MB (proved above) 

∠ B = ∠ C  (60° each)

BC = BC  (common)

∴ Δ BNC and Δ CMB  (SAS)

∴ BN = CM   (CPCT)