Mathematics - Properties of Triangle Question with Solution | TestHub

Construct a triangle of sides 3,4,5 with an interior point P whose distances to vertices are x,y,z and whose central angles between corresponding radial segments are 150°,90°,120°. The three given equations are the cosine rules for the three small triangles. Their areas sum to 6: 6=(1/2)xy sin150°+(1/2)yz sin90°+(1/2)xz sin120° =xy/4+yz/2+$\sqrt{3xz}$/4. Multiply by 4 to get 24. Numerical positive solution also verifies ≈24.