Difference between revisions of "2013 AMC 10B Problems/Problem 23"
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In triangle <math>ABC</math>, <math>AB = 13</math>, <math>BC = 14</math>, and <math>CA = 15</math>. Distinct points <math>D</math>, <math>E</math>, and <math>F</math> lie on segments <math>\overline{BC}</math>, <math>\overline{CA}</math>, and <math>\overline{DE}</math>, respectively, such that <math>\overline{AD} \perp \overline{BC}</math>, <math>\overline{DE} \perp \overline{AC}</math>, and <math>\overline{AF} \perp \overline{BF}</math>. The length of segment <math>\overline{DF}</math> can be written as <math>\frac{m}{n}</math>, where <math>m</math> and <math>n</math> are relatively prime positive integers. What is <math>m + n</math>? | In triangle <math>ABC</math>, <math>AB = 13</math>, <math>BC = 14</math>, and <math>CA = 15</math>. Distinct points <math>D</math>, <math>E</math>, and <math>F</math> lie on segments <math>\overline{BC}</math>, <math>\overline{CA}</math>, and <math>\overline{DE}</math>, respectively, such that <math>\overline{AD} \perp \overline{BC}</math>, <math>\overline{DE} \perp \overline{AC}</math>, and <math>\overline{AF} \perp \overline{BF}</math>. The length of segment <math>\overline{DF}</math> can be written as <math>\frac{m}{n}</math>, where <math>m</math> and <math>n</math> are relatively prime positive integers. What is <math>m + n</math>? | ||
Revision as of 16:49, 21 February 2013
Problem
In triangle , , , and . Distinct points , , and lie on segments , , and , respectively, such that , , and . The length of segment can be written as , where and are relatively prime positive integers. What is ?