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Let a circle with centre at C be made to pass through the point P(1,2), touching the straight lines 7x - y = 5 and x + y + 13 = 0 at A and B respectively. If tangents at A and B intersect at Q, then

(A) area of quadrilateral ACBQ can be 100 sq. units

(B) radius of circle can be 40

(C) area of quadrilateral ACBQ can be 200 sq. units

(D) radius of circle can be 10

1 Answer

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Correct option (A) area of quadrilateral ACBQ can be 100 sq. units


Clearly, the point lies on 7x - y = 5

Also, centre of the circle must lie on the bisectors of the lines x + y + 13 = 0 and 7x - y - 5 = 0 given by

Let (h,k) be the centre of the circle, then h -3k = 35 ..... (1) and 3h + k +15 = 0 ..... (2)

Clearly CA is perpendicular AQ

Therefore area of quadrilateral ACBQ

units = 100 sq. units. Hence (A)

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