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 .

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 ^-^!