Answer to Question #302187 in Trigonometry for ABRAHAM SALOMO P

Question

Qn 6. Let A, B, C and D be four points on a circle, taken in such a way that

the segments AC and BD have an intersection E. If AE = πDE, compute,

providing your working, the ratio between the areas of the triangles △AEB

and △CED, that is,

A(△AEB)

A(△CED)

Answer 1

$\angle A= \angle D$ ( angle subtended by an arc BC)

$\angle DEC= \angle AEB$ ( Vertically opposite angles)

$\therefore$ Triangle AED is similar to triangle DEC

Linear scale factor $=\frac {AE}{DE}=\pi$

$\implies$ Area scale factor$= \pi^2$

Area of triangle AEB to area of triangle CED

$= \pi^2:1$