Question

ABCD is a square of side 8, M is the centre of the circle taking AD as diameter , E is a point on the side AB such that CE is a tangent to the circle . Find the area of C​

Answer 1

Step-by-step explanation:

As the square is aligned along the axes so the centre of the circle will be the mid point of AC

⇒ Centre O=(

2

a

,

2

a

)

AC=

(a−0)

2

+(a−0)

2

=

2

a

Radius of circle =r=

2

AC

=

2

2

a

=

2

a

So, the equation of circle with centre O and radius r is

(x−

2

a

)

2

+(y−

2

a

)

2

=(

2

a

)

2

x

2

+

4

a

2

−ax+y

2

+

4

a

2

−ay=

2

a

2

x

2

+y

2

−ax−ay=0

x

2

+y

2

=a(x+y)

Hence proved.

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