(a) A circle with center O has two chords AB and BC which meet at a point P outside the
circle. If ∠AOC = 43◦ and ∠BP D = 18◦
, find the value of ∠BOD.
(b) ABCD is a cyclic quadrilateral within a circle of radius r. The bisector of the angle A
cuts the circle at point P and the bisector of angle C cuts the circle at point Q. The prove that
P Q = 2r
(c) In 4ABC, AD and BE are medians on BC and AC respectively. If ∠CAD = ∠CBE =
30◦
, prove that 4ABC is equilateral.
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