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Mathematics - Circle Question with Solution | TestHub

MathematicsCircleChord, Intercept (Made by the circle)Medium2 minQB

MathematicsMediummultiple choice

Lines $x / a + y / b = 1$ and $x / c + y / d = 1$ meet the axes at four concyclic points. Suppose $a, b, c, d > 0, a^{2} + c^{2} = b^{2} + d^{2}$ , and the two lines have a unique intersection. The lines can meet at

Options:(select one or more)

Answer:

A, D

Solution:

Concyclic axis intercepts require $ac = bd$ . Equality of the sums of squares then makes the positive unordered pairs ${a, c}$ and ${b, d}$ equal. For distinct lines the intercepts swap, forcing $x = y > 0$ . Choose scaled swapped intercepts to obtain either $(1, 1)$ or $(3, 3)$ .

Stream:JEESubject:MathematicsTopic:CircleSubtopic:Chord, Intercept (Made by the circle)

⏱ 2mℹ️ Source: QB

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