Key idea: Calculate the area of ADE and CDE triangle. Sum of the area of two triangles will be the area of ADCE quadrilateral. By subtracting area of sector ADE of the circle from the the ADCE quadrilateral we can get the area of CEBD portion.

Detail Explanation: As the value of AF and FD will be given we can find the length of AD(which is radius of the circle) by Pythagorian theorem. AD=sqrt(AFAF + FDFD).
Now we can find the angle DAF = tan^-1(FD/AF).
As the tangent create right angle with the center we can say that ADC is a right angled triangle. So the length of AC = AD/sin(DAC) ( Here DAC=DAF as F is a point in AC segment)
Now the Area of ADE triangle = (½ * DEAF)
and the Area of CDE triangle = (½ * DE
(AC-AF))
The area of ADCE quadrilateral = ADE + CDE
The angle DAE = 2DAF. So the area of sector ADE= ½ * ADAD*(angle DAE)

So the area of CEBD portion = area of ADCE quadrilateral - area of sector ADE

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bisnu_sarkarEarliest, Aug '20
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