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Example – 1 In the adjoining figure, the diameter CD of a circle with centre O is perpendicular to the chord AB. If AB = 12cm and CE = 4cm, find the radius of the circle.

Solution : AE = BE = 6cm

Example – 2 A triangle ABC with AB = AC = 10cm and BC = 12cm has been inscribed in a circle. Find the radius of the circle.

Solution : AL is drawn perpendicular to BC.

As, AB = AC

Centre of the circle O will lie on AL as AL is the perpendicular bisector of BC. OB is joined

From right angled triangle ABL, AB² = BL² AL²,[By Pythagoras Theorem]

Or, AL² = AB² – BL²
            = 10² – 6² = 64

AL = 8

OL = AL – OA = 8 – r

From right angled triangle BOL,

OB² = BL² + OL² ,[ By Pythagoras Theorem]

r² = 6² + (8 - r) ²

or, r² = 36 + 64 – 16r + r²

or 16r = 100

or r = 6.25

radius is 6.25cm