It is known that in △ ABC, ab = AC, ⊙ o with ab as diameter intersects BC at D and AC at e. it is proved that △ Dec is an isosceles triangle Such as the title

It is known that in △ ABC, ab = AC, ⊙ o with ab as diameter intersects BC at D and AC at e. it is proved that △ Dec is an isosceles triangle Such as the title

Because ⊙ o with ab as diameter intersects with BC at D, and intersects with AC at e, so the angle AEB = angle ADB = 90 degrees, because AB = AC, so the triangle ABC is isosceles triangle, because the angle ADB = 90 degrees, so ad is the height of BC at the bottom of isosceles triangle, so BD = DC, because the angle AEB = 90 degrees, so the angle BEC = 180-90 = 90 degrees, so the triangle