In a circle with center O, the diameter AC is drawn and the chord BD intersects

In a circle with center O, the diameter AC is drawn and the chord BD intersects at point M with BM = DM Angle BAC = 35 degrees Find the angle BAD.

Since, by condition, BM = DM, the diameter of the AC is perpendicular to the chord BD.

Then the triangles AMD and ABM are rectangular, in which the legs DM and BM are equal, and the leg AM is common, then the right-angled triangles AMD and ABM are equal in two legs. Then the angle MAD = MAB = 35, and the angle BAD = MAD + MAB = 35 + 35 = 70.

Answer: The angle BAD is 70.