x Turn on thread page Beta
 You are Here: Home >< Maths

# (somewhat) Simple geometry problem watch

1. http://gogeometry.com/school-college...ngent-area.htm

I have reduced the problem to proving that HB/r = BC/BG not sure if thats actually harder or easier to prove

also I've tried taking the meeting point of the lines to infinity and showing that its true for that case, and then trying to prove that moving the lines does not change the ratio, but I couldn't

any ideas?
2. (Original post by physics4ever)
http://gogeometry.com/school-college...ngent-area.htm

I have reduced the problem to proving that HB/r = BC/BG not sure if thats actually harder or easier to prove

also I've tried taking the meeting point of the lines to infinity and showing that its true for that case, and then trying to prove that moving the lines does not change the ratio, but I couldn't

any ideas?
So this actually reduces into something nicer. Point P is pretty much irrelevant. So you want to prove that HB/r=BC/BG, but if you extend PH to meet AE at J, then BC/BG=AE/EJ=2r/EJ. Now it's a problem about a circle, its circumscribed square and a tangent to that circle. So now you want to prove HB/r=2r/EJ, or HB*EJ=2r^2. Now you look at areas
3. (Original post by Renzhi10122)
So this actually reduces into something nicer. Point P is pretty much irrelevant. So you want to prove that HB/r=BC/BG, but if you extend PH to meet AE at J, then BC/BG=AC/EJ=2r/EJ. Now it's a problem about a circle, it's circumscribed square and a tangent to that circle. So now you want to prove HB/r=2r/EJ, or HB*EJ=2r^2. Now you look at areas
bae

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: February 15, 2016
Today on TSR

### Boyfriend slept with someone else

...we were on a break

Poll
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams