1. Chords AE & BF when produced intersect at D, AF, BE are joined intersecting each other at G. OA & OB are joined. show x = y + z (see figure) (with alternate solution)
2. Two circles with centres O and O' intersect each other at B & C. OC is joined and produced both ways intersecting the circles at A and D respectively. Find angle B'OD(see figure)
3. Diagonals of a cyclic quadrilateral are perpendicular to each other. Prove that the perpendicular from their point of intersection on any side when produced backwards bisects the opposite side.
5. Let the vertex of an angle ABC be located outside a circle and the sides of the angle intersect equal chords AD and CE with the circle. Prove that angle ABC is equal to half the difference of the angles subtended by the chords AC and DE at the centre.
