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European Girls' Mathematical Olympiad
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In a triangle ABC, the angle bisector of angle A intersects the side BC at point D. If AB = 10 cm, AC = 12 cm, and AD = 8 cm, find the length of BD.
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A
6 cm
💡 Explanation:
Using the Angle Bisector Theorem, we have BD/DC = AB/AC. Substituting the given values, we get BD/DC = 10/12. Solving for BD, we get BD = 10/12 * DC. Since DC = BC - BD, we have BD = 10/12 * (12 - BD). Solving for BD, we get BD = 6 cm.