# In the figure (i) given below, O is the centre of the circle. AB and CD are the chords of the circle. OM is perpendicular to AB and ON is perpendicula

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In the figure (i) given below, O is the centre of the circle. AB and CD are the chords of the circle. OM is perpendicular to AB and ON is perpendicular to CD. AB=24 cm OM=5 cm, ON=12 cm. Find the, (i) radius of the circle (ii) length of chord CD (ii) In the figure (ii) given below, CD is diameter which meets the chord AB at E such that AE = BE = 4 cm.If CE = 3 cm, find the radius of the circle.

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In triangle OAM
OA^2=OM^2+AM^2
r^2=5^2+12^2
r^2=169
r=13
IntriangleONC
OC^2=ON^2+NC^2
NC^2=169-144
NC=5
So,
CD=10cm
IntriangleOBE
OB^2=OE^2+BE^2
r^2=(r-3)^2+4^2
solving this we get
r=25/6cm