CAT 2023 Slot 1 QA Question 17: A quadrilateral ABCD is inscribed in a circle such that $AB:CD = 2:1$ and $BC:AD = 5:4$. If AC and BD intersect at the point E, then $AE:CE$ equals

Question

A quadrilateral ABCD is inscribed in a circle such that $AB:CD = 2:1$ and $BC:AD = 5:4$. If AC and BD intersect at the point E, then $AE:CE$ equals

Accepted Answer

Since ABCD is cyclic and E is the intersection of the diagonals, the following pairs of triangles are similar.

△ABE ∼ △DCE
$\dfrac{AE}{DE} = \dfrac{AB}{CD} = \dfrac{2}{1}$
$AE = 2DE$

Also,
△BCE ∼ △ADE
$\dfrac{CE}{DE} = \dfrac{BC}{AD} = \dfrac{5}{4}$
$CE = \dfrac{5}{4} DE$

Therefore,
$AE:CE = 2DE:

A quadrilateral ABCD is inscribed in a circle such that AB:CD=2:1AB:CD = 2:1AB:CD=2:1 and BC:AD=5:4BC:AD = 5:4BC:AD=5:4. If AC and BD intersect at the point E, then AE:CEAE:CEAE:CE equals