In the figure above, CD is the diameter which meets the chord AB in E such that AE=BE=4cm. If CE = 3cm, find the radius of the circle.
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Given:
Diameter = CD
AE=BE=4cm
CE = 3cm
To Find:
Radius of the circle.
Solution:
As O is the centre of circle, we will join OA
Thus, OE⊥AB
Let,OC = OA = x = ( Radius of circle)
OE =OC−EC = (x−3)
InΔOEA
By Pythagoras Theorum,
OA² + OE² + AE²
= x² = ( x - 3)² + 4²
= x² - 6R + 9 + 16 = x²
= x² - x² - 6x = - 25
= 6x = 25
= x = 25/6
= x = 4.16
Answer: The radius of the circle is = 4.16cm
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