# Proof in circles and tangents?

1. Sep 24, 2011

### 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.

2. Sep 24, 2011

### Staff: Mentor

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

3. Sep 25, 2011

### vkash

how?? which triangles??

4. Sep 25, 2011

### Staff: Mentor

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

5. Sep 25, 2011

### 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.

6. Sep 27, 2011

### 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

7. Sep 30, 2011

### vkash

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