- #1
mrtwhs
- 47
- 0
Let \(\displaystyle \triangle ABC\) be a right triangle with right angle at \(\displaystyle C\). Suppose this right triangle has legs \(\displaystyle BC=a\), \(\displaystyle AC=b\), hypotenuse \(\displaystyle AB=C\), and circumradius \(\displaystyle R\). Two copies of this triangle can be joined to form an isosceles triangle in two ways. With \(\displaystyle a\) as a common side, you can form an isosceles triangle with sides \(\displaystyle c,c,2b\) and circumradius \(\displaystyle R_1\). With \(\displaystyle b\) as a common side, you can form an isosceles triangle with sides \(\displaystyle c,c,2a\) and circumradius \(\displaystyle R_2\). Find a formula relating \(\displaystyle R,R_1,R_2\).