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Question

An isosceles right angled triangle is inscribed in the circle x2+y2=r2. If the coordinates of an end of the hypotenuse are (a, b), the coordinates of the vertex are


A
(-a, -b)
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B
(b, -a)
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C
(b, a)
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D
(-b, -a)
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Solution

The correct option is B (b, -a)


Since the hypotenuse of a right angled triangle inscribed in a circle is a diameter of the circle. If the coordinates of the end C of the hypotenuse BC are (a, b), the coordinates of B are (-a, -b). Equation of BC is yx=ba. If A is the vertex of the isosceles triangle, then OA is perpendicular to BC and the equation of AO is yx=ab which meets the circles x2+y2=r2 at points for which
(a2b2+1)x2=r2=a2+b2 [(a,b) lies on x2+y2=r2]x2=b2x=±b y=a Coordinates of A are (b,a) or (b,a).


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