Pretty basic Pythagorean & Trigonometry

[DenisKurek]

Hi,

It's probably gonna be a pretty simple thing to solve for you but I'm not that good in math so I'm really thankful for any help that you can bring me.

Long story short (refer picture below):

As you can see we have two circles forming two right angled triangles with a third one. The information in white are the ones I know and the ones in the red are the ones I'm looking for. So given the coordinates a and b, and the lengths ab, bc and ac, is it possible to find the coordinates of the point c in the right angled triangle abc.
Then, if it's possible to have the coordinate of c, is it possible to find the coordinate of the point d with the information we have?

 

[firemath]

Use the tangent ratio. Then you can find the length of CD. Is this what you are asking?

 

[pka]

Hi,

It's probably gonna be a pretty simple thing to solve for you but I'm not that good in math so I'm really thankful for any help that you can bring me.

Long story short (refer picture below):

As you can see we have two circles forming two right angled triangles with a third one. The information in white are the ones I know and the ones in the red are the ones I'm looking for. So given the coordinates a and b, and the lengths ab, bc and ac, is it possible to find the coordinates of the point c in the right angled triangle abc.
Then, if it's possible to have the coordinate of c, is it possible to find the coordinate of the point d with the information we have?

I have spent time thinking about your question. Frankly I don't know if the coordinates are actually numerical numbers or just abstract.
Here are some random thoughts.
\(\displaystyle \begin{gathered}
{({x_a} - {x_c})^2} + {({y_a} - {y_c})^2} = {(ac)^2} \hfill \\
{({x_a} - {x_b})^2} + {({y_a} - {y_b})^2} = {(ab)^2} \hfill \\
{({x_b} - {x_c})^2} + {({y_b} - {y_c})^2} = {(bc)^2} \hfill \\
{(ac)^2} + {(bc)^2} = {(ab)^2} \hfill \\ \end{gathered} \)
If I were you, I might look at the equation of a circle centered at \(\displaystyle (x_a,y_a\) with radius \(\displaystyle (ac)\).
That circle is tangent to \(\displaystyle \overline{bd}\) at the point \(\displaystyle \bf c\).
Please try to post what you find.