Geometry help please!!!

[Sir_Laughalot]

Man...I hate geometry....I feel like when I see them...

I can still do them but I can't do these :sick: .

Please help me and diagrams would be nice ;) .

A circle is drawn so that it just fits in the corner of a page. Point A is 1cm from one edge of the page and 2cm from another edge. Find the radius of the cricle.

Two circles of the same radius touch at A and have a common tangent BC. A small circle touches the larger circles and also has BC as a tangent. Prove that the radius of the small circle is 1/4 of the radius of the larger circles.

P is a point within a rectangular room ABCF. P's distance to A, B and C is 4m, 3m and 2m respectively. Find distance DP.

[Logophobic]

1) I'm assuming that point A is on the circle. Placing the corner of the page at the origin puts the center of the circle at (r,r) and point A at (2,1). The distance from the center to point A is r.

r = Sqr((r-2)2+(r-1)2)
r2 = (r-2)2+(r-1)2
r2 = (r2-4r+4)+(r2-2r-1)
0 = r2 - 6r + 5
0 = (r - 5)(r - 1)
r = 5 or r = 1

2) See diagram.

(R - r)2 + R2 = (R + r)2
(R2 - 2Rr + r2) + R2 = R2 + 2Rr + r2
2R2 - 2Rr + r2 = R2 + 2Rr + r2
R2 - 2Rr = 2Rr
R - 2r = 2r
R = 4r

3) See diagram.

a2 + d2 = 42 = 16
a2 + b2 = 32 = 9
b2 + c2 = 22 = 4
c2 + d2 = DP2

a2 + d2 = 16
a2 + b2 = 9
d2 - b2 = 7

c2 + d2 = DP2
b2 + c2 = 4
d2 - b2 = DP2 - 4

DP2 - 4 = 7
DP2 = 11
DP = Sqr(11)

Edit: I mixed up the files - Q2.jpg is for #3, and Q3.jpg is for #2

[Sir_Laughalot]

oh....dang, I should have used graphs....

But thanks anyway Logico ^-^!