The chords AB and CD are drawn in the circle. Find the angle BDC if the angle is ACD = 15

The chords AB and CD are drawn in the circle. Find the angle BDC if the angle is ACD = 15 degrees, AB is perpendicular to CD.

Since the chord AB is perpendicular to the chord CD, the triangle AOC is rectangular.

Then, in a right-angled triangle AOC, the angle OAC = (180 – 90 – 15) = 75.

The angle OAC of the AOC triangle is equal to the inscribed angle BAC. The inscribed angle BAC rests on the BC arc.

The sought angle BDC is also based on the arc BC, then the angle BDC = BAC = 75.

Answer: The BDS angle is 75.