JEE Mains · Maths · STD 11 - 10.1 circle and system of circle
Let the tangent to the circle \(x^{2}+y^{2}=25\) at the point \(R (3,4)\) meet \(x\) -axis and \(y\) -axis at point \(P\) and \(Q\), respectively. If \(r\) is the radius of the circle passing through the origin \(O\) and having centre at the incentre of the triangle \(OPQ ,\) then \(r ^{2}\) is equal to
- A \(\frac{529}{64}\)
- B \(\frac{125}{72}\)
- C \(\frac{625}{72}\)
- D \(\frac{585}{66}\)
Answer & Solution
Correct Answer
(C) \(\frac{625}{72}\)
Step-by-step Solution
Detailed explanation
Tangent to circle \(3 x+4 y=25\) \(OP + OQ + OR =25\) In centre \(=\left(\frac{\frac{25}{4} \times \frac{25}{3}}{25}, \frac{\frac{25}{4} \times \frac{25}{3}}{25}\right)\) \(=\left(\frac{25}{12}, \frac{25}{12}\right)\)…
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