2. Perpendicular from centre bisects chord
The perpendicular from the centre of a circle to a chord bisects the chord.












In the diagram, ON perpendicular AB
Then AN=BN


Example:
In the diagram, AB and CD are two parallel chords of a circle, centre O. AB=30 cm, CD= 48cm and the perpendicular distance from O to AB is 20cm. Find
a) the radius of the circle,
b) the perpendicular distance between AB and CD














Solutions:
a) Draw the radii OA and OC. Draw the perpendicular ON from O to CD. Since AB//CD, MON is a straight line.

In triangle OAM,

AM=1/2 AB
= 1/2 x 30
= 15cm (perpendicular from centre bisects chord)

OA square = AM square + OM square
OA = Square root 625
= 25cm (pyth thm)

The radius of the circle is 25cm.

a) In triangle OCN,
CN = 1/2CD
= 1/2 x 48
= 24cm

OC square = CN square + ON square
25 square = 24 square + ON square
ON square = 49
ON = 7cm (pyth thm)

Perpendicular distance between AB and CD = MO + ON
= 20 + 7
= 27cm