In the adjoining figure, $$AB$$ is a diameter of the circle. Given $$\angle BAC=20^\circ$$ and $$\angle AEB=56^\circ$$, the measure of $$\angle BCD$$ in degrees is

Since $$AB$$ is a diameter, $$\angle ACB=90^\circ$$. Points $$A$$, $$C$$ and $$E$$ are collinear, so triangle $$AEB$$ gives $$\angle ABE=180^\circ-20^\circ-56^\circ=104^\circ$$, and because $$E$$, $$B$$ and $$D$$ are collinear, $$\angle ABD=76^\circ$$. Also $$\angle ADB=\angle ACB=90^\circ$$ because both subtend chord $$AB$$. Hence $$\angle BAD=180^\circ-76^\circ-90^\circ=14^\circ$$, and $$\angle BCD=\angle BAD=14^\circ$$ because both subtend chord $$BD$$.