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Omni-MATH / Let ABCD be a cyclic quadrilateral, and let segments AC and BD intersect at E. Let W and Y be the feet of the altitudes from E to sides DA and BC, respectively, and let X and Z be …

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problem

Let ABCDA B C D be a cyclic quadrilateral, and let segments ACA C and BDB D intersect at EE. Let WW and YY be the feet of the altitudes from EE to sides DAD A and BCB C, respectively, and let XX and ZZ be the midpoints of sides ABA B and CDC D, respectively. Given that the area of AEDA E D is 9, the area of BECB E C is 25, and ∠EBC−∠ECB=30∘\angle E B C-\angle E C B=30^{\circ}, then compute the area of WXYZW X Y Z.
Plain-text mathematical notation (without MathML)
Let ABCD be a cyclic quadrilateral, and let segments AC and BD intersect at E. Let W and Y be the feet of the altitudes from E to sides DA and BC, respectively, and let X and Z be the midpoints of sides AB and CD, respectively. Given that the area of AED is 9, the area of BEC is 25, and ∠EBC−∠ECB=30^(∘), then compute the area of WXYZ.
Original LaTeX notation
Let $A B C D$ be a cyclic quadrilateral, and let segments $A C$ and $B D$ intersect at $E$. Let $W$ and $Y$ be the feet of the altitudes from $E$ to sides $D A$ and $B C$, respectively, and let $X$ and $Z$ be the midpoints of sides $A B$ and $C D$, respectively. Given that the area of $A E D$ is 9, the area of $B E C$ is 25, and $\angle E B C-\angle E C B=30^{\circ}$, then compute the area of $W X Y Z$.

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Source and history

task_id
3737487a-7cb6-5553-a8a3-10fef65d7a16
task_key
test--3737487a-7cb6-5553-a8a3-10fef65d7a16
task_revision_id
1
config / split
/ test

Official source

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