Category: Geometry
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Problem Let ABC be triangle in which AB = AC. Suppose the orthocentre of the triangle lies on the incircle. Find the ratio AB/BC Solution Method 1 Proof: Given AB=AC, AD is perpendicular bisector of BC and angle bisector of So, incenter and orthocenter lies on AD Since H (Orthocenter) lies on incircle But and…
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1. Problem The in-circle of triangle ABC touches the sides BC, CA and AB in K, L and M respectively. The line through A and parallel to LK meets MK in P and the line through A and parallel to MK meets LK in Q. Show that the line P Q bisects the sides AB…
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1. Problem Let P be an interior point of a triangle ABC and AP, BP, CP meet the sides BC, CA, AB in D, E, F respectively. Show that 2. Solution Proof: = area of figure Since height from C to base is same for both AFC and BFC (proof in Lemma 1) Since height…
The Mathematical Pursuit 