﻿ If O is the origin and OP, OQ are distinct tangents to the circle x2 + y2 + 2gx + 2fy + c = 0, the circumcentre of the triangle OPQ is : Kaysons Education

# If O is The Origin And OP, OQ are Distinct Tangents To The Circle x2 + y2 + 2gx + 2fy + c = 0, The Circumcentre Of The Triangle OPQ is

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## Question

### Solution

Correct option is

None of these.

Since PQ is the chord of contact of the tangents from the origin O to the circle

x2 + y2 + 2gx + 2fy + c = 0,                        (1)

equation of PQ is

gx + fy + c = 0                                             (2)

An equation of a circle through the intersection of (1) and (2) is given by

If the circle (3) passes through O, the origin, then c + λc = 0, i.e.,

λ = –1, and the equation of the circle (3)

becomes               x2 + y2 + gx + fy = 0

Centre of the circle is (–g/2, –f/2), and hence it is the circumcentre of the triangle OPQ.

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