Proof in circles and tangents?

[vkash]

there is a circle say S₁,there is a point P outside circle. Two tangents are drawn from the point P to the circle. These two tangents touches circles S₁ at Q and R. A circle is made through P,Q,R. proof that circle is passing through center of S₁.

I have tried to put some triangles congruent similar and some other ideas but all failed.

 

[NascentOxygen]

For starters, I see congruent triangles (Right-angle, Hypotenuse, Side).

 

[vkash]

For starters, I see congruent triangles (Right-angle, Hypotenuse, Side).

how?? which triangles??

 

[NascentOxygen]

You have tangents to a circle? Then there are your right-angles.

 

[HallsofIvy]

Draw the line from the given point to the center of the circle. Draw the radii from the center of the circle to the points of tangency. There are your triangles. Also use the fact that if two vertices of a triangle lie on the ends of a diameter of a circle and the third vertex is on the circle, then the angle at that third point is a right angle.

 

[zgozvrm]

Obviously, the midpoint of S₁P (let's call it T) is equidistant from both S₁ & P (by definition of midpoint).

That is, TS₁ = TP

All you need to do is first show that PQ = PR, then show that TP = TQ = TS₁

 

[vkash]

this is so simple question. i did not got the point. thanks to all answerers.
sorry for late reply.