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If points Aa n dB are (1, 0) and (0, 1),...

If points `Aa n dB` are (1, 0) and (0, 1), respectively, and point `C` is on the circle `x^2+y^2=1` , then the locus of the orthocentre of triangle `A B C` is (a) `x^2+y^2=4` (b) `x^2+y^2-x-y=0` (c) `x^2+y^2-2x-2y+1=0` (d) `x^2+y^2+2x-2y+1=0`

Text Solution

Verified by Experts

The correct Answer is:
`x^(2)+y^(2)-2x-2y+1=0`

Let `C-= ( cos theta, sin theta) , H(h,k)` is the orthocenter of `Delta ABC`.
Since the circumcenter of the triangle is (0,0), for the orthocenter `h=1+cos theta` and `k=1+sin theta`
Eliminating `theta`
`(x-1)^(2)+(y-1)^(2)=1`
or `x^(2)+y^(2)-2x-2y+1=0`
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