perplexus.info :: Geometry : Circle in a trapezoid

Circle in a trapezoid (Posted on 2023-12-11)

A circle is inscribed in an isosceles trapezoid ABCD.The diagonal AC intersects the circle at K and L, in the order A,K,L,C.

Find the value of ((AL * KC)/(AK * LC))^1/4.

No Solution Yet Submitted by Danish Ahmed Khan

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Drawing with possible answer

| Comment 1 of 2

https://www.desmos.com/geometry/qilqesyfcc

The answer appears to be the constant 1+sqrt(2)

I tried to solve analytically, hence Desmos/Geometry but I quickly resorted to synthetically. Unfortunately the algebra then got to be crazy.

Note I found the distances using the x-coordinates only, since we are finding a ratio and the true distance is just a scale factor that will reduce away.

Posted by Jer on 2023-12-12 15:19:02

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