# Surveying Problem Relating To Circles & Lines

1. Dec 11, 2013

### tomtomtom1

Hello all

I am hoping someone could help shed some light on a surveying problem I am having.

The problem is this:-

• A circle is centered at point B with Known co-ordinates (X2,Y2)
• The circle has a radius which is known (R).
• Point A lays outside of the circle with known co-ordinates (X1,Y1)
• A line is connected between Point A and Point B.
• Point C lays on the line between Point A & B.
• Point C also lays at the exact intersection of where the line and the circle meet.
• The distance between Point A and Point C is known (S).
• All points are in a Cartesian co-ordinate system

Work out what are the co-ordinates of Point C.

I have attached a diagram of the problem.

Can anyone help?

#### Attached Files:

• ###### circle problem.pdf
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2. Dec 11, 2013

### cpscdave

You should be able to solve this using TRIG
Look at the triangle X2,Y2 X1,Y1, X1,Y2
You can then figure out the angles involved.
Then using similar triangles figure out where point C is :)

3. Dec 11, 2013

### cpscdave

Specifically
$θ = tan^{-1}((Y1-Y2)/(X1-X2))$

then
$C_x = cos(θ)*R$
$C_y = sin(θ)*R$