Difference between revisions of "2006 iTest Problems/Problem U8"
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==Problem== | ==Problem== | ||
− | Cyclic quadrilateral <math>ABCD</math> has side lengths <math>AB = | + | Cyclic quadrilateral <math>ABCD</math> has side lengths <math>AB = 9</math>, <math>BC = 2</math>, <math>CD = 3</math>, and <math>DA = 10</math>. Let <math>M</math> and <math>N</math> be the midpoints of sides <math>AD</math> and <math>BC</math>. The diagonals <math>AC</math> and <math>BD</math> intersect <math>MN</math> at <math>P</math> and <math>Q</math> respectively. <math>\frac{PQ}{MN}</math> can be expressed as <math>\frac{m}{n}</math> where <math>m</math> and <math>n</math> are relatively prime positive integers. Determine <math>m + n</math>. |
Revision as of 19:44, 23 February 2021
Problem
Cyclic quadrilateral has side lengths
,
,
, and
. Let
and
be the midpoints of sides
and
. The diagonals
and
intersect
at
and
respectively.
can be expressed as
where
and
are relatively prime positive integers. Determine
.