1. Let ABC be a triangle. Let D, E, F be points on the segments BC, CA and AB such that AD, BE and CA concur at K. Suppose $latex (\frac{BD}{DC} = \frac{BF}{FA})$ and ∠ADB = ∠AFC. Prove that ∠ABE = ∠CAD. Solution: Diagram Given: ABC be any triangle. AD, BE and CF are drawn […]
ABCD is a quadrilateral and P, and Q are mid-points of CD, and AB respectively. Let AP, DQ meet at X, and BP, CQ meet at Y . Prove that area of ADX + area of BCY = area of quadrilateral PXQY The number of ways in which three non-negative integers \( n_1, n_2, n_3 […]
Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1994 based on Length and Inequalities.
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Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1995 based on GCD and Ordered pair.