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In OD, AB = CB and marc CE - 52. Find mZBCE. (See picture)

A. 109

Step-by-step explanation:

We know that since AB = CB, then ΔABC is isosceles.

Since AC, one of the sides of ΔABC, is on the diameter of circle D, by definition, we know that ΔABC is also a right triangle. Thus, if ΔABC is an isosceles right triangle, then ∠BAC = ∠BCA = 45°.

Draw a line connecting D to B so that we now have isosceles triangle BDC. Since arc BC is 52°, by definition of central angles, ∠BDC is also equal to 52°. Then, ∠DBC = ∠DCB = (180 - 52)/2 = 64°.

∠BCE = ∠DCB + ∠BCA

∠BCE = 64 + 45 = 109°

The answer is thus A.

~ an aesthetics lover

m = 8

n = 40°

Step-by-step explanation: