Let origin lies inside the circle . A PQ chord through origin is such that then the radius of the circle is

Question

Let origin lies inside the circle $x^{2} + y^{2} - x - \sqrt{2} y - c = c > 0$ . A PQ chord through origin (where P,Q lies on circle) is such that $O P = 2, O Q = 8$ (where O is the origin), then the radius of the circle is

Smart Achievers · Accepted Answer

(3)

$O_{1} O = \sqrt{33}$ and $O M = 3$

$\Rightarrow O_{1} M = 2 \sqrt{6}$ and $P M = 5 \Rightarrow O_{1} P = 7$

Solution

Q.
Let origin lies inside the circle $x^{2} + y^{2} - x - \sqrt{2} y - c = c > 0$ . A PQ chord through origin (where P,Q lies on circle) is such that $O P = 2, O Q = 8$ (where O is the origin), then the radius of the circle is

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4 8

Ans.
(3)

$O_{1} O = \sqrt{33}$ and $O M = 3$

$\Rightarrow O_{1} M = 2 \sqrt{6}$ and $P M = 5 \Rightarrow O_{1} P = 7$

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Solution

Q. Let origin lies inside the circle x2+y2-x-2y-c=c>0. A PQ chord through origin (where P,Q lies on circle) is such that OP=2, OQ=8 (where O is the origin), then the radius of the circle is

1 5

2 6

3 7

4 8

Ans. (3) O1O=33 and OM=3 ⇒O1M=26 and PM=5⇒O1P=7

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Q.
Let origin lies inside the circle $x^{2} + y^{2} - x - \sqrt{2} y - c = c > 0$ . A PQ chord through origin (where P,Q lies on circle) is such that $O P = 2, O Q = 8$ (where O is the origin), then the radius of the circle is

Ans.
(3)

$O_{1} O = \sqrt{33}$ and $O M = 3$

$\Rightarrow O_{1} M = 2 \sqrt{6}$ and $P M = 5 \Rightarrow O_{1} P = 7$