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integer lenght of angle bisector 2020 MBMT p42

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February 13, 2022
geometryangle bisectorMBMT

Problem Statement

△ABC\vartriangle ABC has side lengths AB=4AB = 4 and AC=9AC = 9. Angle bisector ADAD bisects angle AA and intersects BCBC at DD. Let kk be the ratio BDAB\frac{BD}{AB} . Given that the length ADAD is an integer, find the sum of all possible k2k^2 .
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