1) Find the angles X° and Y° in the following diagram in which AP and BP are tangents to the circle and O is its centre.

2) In the following diagram, PC is a tangent to the circle and is of length 8 cm. If BP is of length 5 cm, find the length of AB.

3) Two chords AB and CD of a circle intersect at right angles at P. If AC = 2.5 cm, AP = 2 cm and PB = 2 cm, find the length of PD.

4) In the diagram below, the circle is of radius 5 cm and the chord AB is of length 8 cm.

(a) Using the intersection of two chords property, determine the height h of the minor segment.

(b) Explain why this method gives two values for h.

(c) Confirm your answer by applying Pythagoras’ theorem to triangle OPB.

Transcribed Image Text:

A B 46 P