Tough geometry problem.I've been trying it for hours?

Question

A circle C1 with centre O1 exists. Inside it exists another circle C2 with centre O2 just touching C1 at A.Another circle C3 ,passing through O2 also touches C1 at B meeting C2 at P and Q a line through PQ touches C1 at X and Y.X and Y are joined to B meeting C3 at F and G respectively.Prove that FG is tangent to C2
Please no co ordinates or trignometry

Here a tangent is a line touching a circle at a point

sorry about a line through X and Y.I meant a line joining X and Y

to Benjamin_N
Thats a good conclusion but I figured it out looooong ago

Answer 1

I might be able to help, but I need some clarification on what "X and Y are joined at B meeting C3 at F and G" means. X and Y are points. By your definition above, a line through X and Y only intersects C3 at P and Q.

Answer 2

( stares wide eyed drooling slighty) dude hold on i think i can do this tell what the chapter is your working on like so i can get a category and then i will get the answer and edit my thingy

There are two definitions of tangent in geometry: First, a tangent line is a line that touches a curve at one point, but does not cross the curve. Both curves and straight lines can be tangent to another curve.

A tangent to a circle is perpendicular to the radius drawn to the point of tangency. You will find a good proof of this in your geometry book. The diagram is too difficult for me to draw here.

In a right triangle, the tangent of an angle is the ratio of the side opposite the acute angle to the side adjacent. Remember, a right triangle has two sides and an hypotenuse.

ok so bsed on that i could say that ummmm yeha i still dont know i am taking geometry but let me explain my teacher told us he was the only teacher that could count three weeks because every other teacher gave us our three weeks grade a girl got out a calender and showed him that it had been three weeks and he said yeah ill remember that next time i grade your test if that says anyting about his character he tells us the page to work we dont learn anything or i would try to help more i really am sorry that you have to do that problem that sucks toads

Answer 3

Well, for starters, FG || PQ because of similarity. So that establishes that FG is perpendicular to the radius of circle #2. This will be true even if circle #3 does not pass through the center of circle #2, so the remaining thing to prove--the distance from the center of circle #2 of this intersection--has to do with the special requirement on circle #3.

Well, one more comment on this before I retire. The locus of all the possible centers for circle # 3 seems to be an ellipse with foci at O1 and O2, with the distances from center 3 to these points always adding to R1. Good luck, and good night.

Answer 4

Draw it out and read the last chapter of your geometry book doing all sample problems.

Answer 5

Show us the diagram!

Give us a link to the diagram.

Answer 6

Sorry i barely passed that class last year. I can't help.