Segments AB and CD intersect at point O, with AO = BO, CO = DO. Find the angle BDC and AC

Segments AB and CD intersect at point O, with AO = BO, CO = DO. Find the angle BDC and AC if the angle DCA = 70 degrees, BD = 13 cm.

To solve the problem, consider the figure.

According to the condition AO = BO, CO = DO, angle DCA = 70 degrees, BD = 13 cm.

Consider triangles AOC and BOD.

Angle DOB = Angle AOC as cross overlapping angles.

AO = BO, CO = DO.

Then the triangles AOC and BOD are equal in two sides and the angle between them.

AC is parallel to DB because the internal angles are equal.

Then the angle BDC = DCA = 70 and AC = BD = 13 cm.

Answer: BDC = 70, AC = 13 cm.