Question #302187

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)


1
Expert's answer
2022-02-28T17:03:51-0500

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


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


\therefore Triangle AED is similar to triangle DEC


Linear scale factor =AEDE=π=\frac {AE}{DE}=\pi


    \implies Area scale factor=π2= \pi^2

Area of triangle AEB to area of triangle CED


=π2:1= \pi^2:1



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