Hello donut166 Originally Posted by

**donut166** do i solve the final equations u wrote?

these equations:

Read carefully what **red_dog** wrote. To find the circumcentre, you'll need to solve:$\displaystyle (x-82)^2+(y-21)^2=(x-12)^2+(y-27)^2=(x-74)^2+(y-43)^2$

which you'll do by taking, say, the first two expressions:$\displaystyle (x-82)^2+(y-21)^2=(x-12)^2+(y-27)^2$

expanding the brackets, and simplifying to obtain a linear equation in $\displaystyle x$ and $\displaystyle y$ (i.e. there won't be any $\displaystyle x^2$ or $\displaystyle y^2$ terms).

Then take the second and third expressions:$\displaystyle (x-12)^2+(y-27)^2=(x-74)^2+(y-43)^2$

and do the same.

Then solve the resulting pair of simultaneous equations.

For the orthocentre, **red_dog** showed you how to find the equation of one of the heights (altitudes) of the triangle. You will need to find a second one in the same way, and then solve this pair of simultaneous equations.

Can you do it now?

Grandad