In △ ABC, a bisector ad intersects BC at point D, and ab = ad, and the extension of CM ⊥ ad intersects ad at point M. am = 1 / 2 (AB + AC)

In △ ABC, a bisector ad intersects BC at point D, and ab = ad, and the extension of CM ⊥ ad intersects ad at point M. am = 1 / 2 (AB + AC)

Lengthen DM to N, make DM = Mn, connect CNAB = ad, know that Δ abd is isosceles triangle, angle ADB = angle B and cm is the vertical line of DN, so Δ CDN is isosceles triangle, angle CDN = angle CND and angle CDN = angle ADB, so the vertex angles of two triangles are equal, that is, angle bad = angle DCN, angle CND = angle CDN = angle ADB = angle DAC + angle ACD, angle ACD = angle ACD +