Difference between revisions of "2020 CIME I Problems/Problem 14"
(Created page with "==Problem 14== Let <math>ABC</math> be a triangle with sides <math>AB = 5, BC = 7, CA = 8</math>. Denote by <math>O</math> and <math>I</math> the circumcenter and incenter of...") |
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==Solution== | ==Solution== | ||
− | Analytic geometry gives us <cmath>DK=\frac{17 \ | + | Analytic geometry gives us <cmath>DK=\frac{17\sqrt57}{19}.</cmath> The answer is <math>93</math>. |
==See also== | ==See also== |
Revision as of 10:55, 1 September 2020
Problem 14
Let be a triangle with sides
. Denote by
and
the circumcenter and incenter of
, respectively. The incircle of
touches
at
, and line
intersects the circumcircle of
again at
. Then the length of
can be expressed in the form
, where
are positive integers,
and
are relatively prime, and
is not divisible by the square of any prime. Find
.
Solution
Analytic geometry gives us The answer is
.
See also
2020 CIME I (Problems • Answer Key • Resources) | ||
Preceded by Problem 13 |
Followed by Problem 15 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
All CIME Problems and Solutions |
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