In the figure,given alongside CD is a diameter which meets the chords AB at E,such that AE=BE=4cm.If CE is 3cm find the radius of the circle.

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Solution

We have $O$ as the centre of circle
join $O A$
we know that line segment joining the centre to the midpoint of the chord is perpendicular to the chord
Now, $O E ⊥ A B$
we have, $L e t, O C = x c m = O A (r a d i i o f t h e c i r c l e) a n d O E = O C - E C = (x - 3) c m I n Δ O E A {O A}^{2} = {O E}^{2} + {A E}^{2} \Rightarrow x^{2} = {(x - 3)}^{2} + 4^{2} \Rightarrow x = \frac{25}{6} \Rightarrow x = 4.16 c m$

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In the figure,given alongside CD is a diameter which meets the chords AB at E,such that AE=BE=4cm.If CE is 3cm find the radius of the circle.

We have O as the centre of circlejoin OAwe know that line segment joining the centre to the midpoint of the chord is perpendicular to the chord Now, OE⊥ABwe have, Let,OC=xcm=OA(radiiofthecircle)andOE=OC−EC=(x−3)cmInΔOEAOA2=OE2+AE2⇒x2=(x−3)2+42⇒x=256⇒x=4.16cm