Question

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Find the coordinates of circumcentre and radius of circumcircle of ∆ ABC if A(7, 1), B(3, 5) and C(2, 0) are given.

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Answer 1

Answer:

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Step-by-step explanation:

Let the circumcentre be

P(a,b)

.

The given points are A(7, 1), B(3, 5) and C(2, 0).

The circumcircle passes through the points A, B and C and the thus,

PA = PB = PC

⇒PA2=PB2=PC2

PA2=PB2

⇒(3−a)2+(5−b)2=(7−a)2+(1−b)2

⇒9+a2−6a+25+b2−10b=49+a2−14a+1+b2−2b

⇒a−b=2.....(1)

PA2=PC2

⇒(7−a)2+(1−b)2=(2−a)2+(0−b)2

⇒49+a2−14a+1+b2−2b=4+a2−4a+b2

⇒5a+b=23.....(2)

(1)+(2)

a=256,b=136

Radius = PC =

=(256−2)2+(136−0)2

=(136)2+(136)2

=1362

Answer 2

Answer:

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