Distance.

[prog_tom]

In the diagram attached,

Find the distance from P to AD.

Notice the curved line from D to B, it's actually a circle, with radius 4, i didn't draw it good. And P is also on a circle with radius 2. There are two circles in the square. AD is 4 units.

I tried to set midpoint M to be (0,0), and P to be (1/4,sqrt(3)/4) since it's not a unit circle, it has a radius of two. And i tried to suppose there was a point T on line AD, which is (-2,sqrt(3)/4). So finding the distance should be easy,

TP = sqrt((x2-x1)^2+(y2-y1)^2)

= sqrt((9/4)^2)
= 9/4

However I think I may be incorrect. Can anyone help me confirming the answer? Thanks.

[krtxmrtz]

Why not directly calculate where the circles have their intersection? The equation of a circle is,

(x - a)2 + (y - b)2 = r2

Your circles have these values:

r = 4, a = 0, b = 4
and
r = 2, a = 2, b = 0

Then,

16 = x2 + (y - 4)2
4 = (x - 2)2 + y2

If you work this out you arrive at the equations

x2 + y2 - 8y = 0
x2 - 4x + y2 = 0

To easily get to the solution, add and substract 2xy to/from each one of them:

x2 + y2 +2xy - 2xy - 8y = 0
x2 - 4x + y2 +2xy - 2xy = 0

This can be rearranged as

(x - y)2 + 2xy -8y = 0
(x - y)2 + 2xy -4y = 0

Now substract one from another and you get

4x - 8y = 0 or x = 2y

Substitute this back into one of the 2 original equations and finally:

4y2 + y2 -8y = 0
y = 8/5 = 1.6 and x = 16/5 = 3.2

[prog_tom]

what are a, and b?

[krtxmrtz]

Originally posted by prog_tom
what are a, and b?
Sorry, forgot about them at the last minute...
They are the x and y coordinates of the center of the circle.