1. In a right triangle, in which, <B=90, a circle is drawn with AB diameter intersecting the hypotenuse AC at P. Prove that the tangent to the circle at P bisects BC. 

2. Tangents PQ and PR are drawn to a circle such that <RPQ=30. A chord RS is drawn parallel to the tangent PQ. Find <QRS.

3. AB is the diameter and AC is a chord of a circle with center O such that <BAC=30. The tangent at C intersects extended AB at D. Prove that BC=BD