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Omni-MATH / Let ABCD be a unit square. A circle with radius (32)/(49) passes through point D and is tangent to side AB at point E. Then DE=(m)/(n), where m,n are positive integers and …

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problem

Let ABCDA B C D be a unit square. A circle with radius 3249\frac{32}{49} passes through point DD and is tangent to side ABA B at point EE. Then DE=mnD E=\frac{m}{n}, where m,nm, n are positive integers and gcd(m,n)=1\operatorname{gcd}(m, n)=1. Find 100m+n100 m+n.
Plain-text mathematical notation (without MathML)
Let ABCD be a unit square. A circle with radius (32)/(49) passes through point D and is tangent to side AB at point E. Then DE=(m)/(n), where m,n are positive integers and gcd(m,n)=1. Find 100m+n.
Original LaTeX notation
Let $A B C D$ be a unit square. A circle with radius $\frac{32}{49}$ passes through point $D$ and is tangent to side $A B$ at point $E$. Then $D E=\frac{m}{n}$, where $m, n$ are positive integers and $\operatorname{gcd}(m, n)=1$. Find $100 m+n$.

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Source and history

task_id
5e47c491-c4da-5aa0-b5a9-5d11dd4e910f
task_key
test--5e47c491-c4da-5aa0-b5a9-5d11dd4e910f
task_revision_id
1
config / split
/ test

Official source

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