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BasicGeom nov 21 - PEM Level C 21 November 2009 Topics in...

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PEM Level C 21 November 2009 Topics in Geometry - Basic Concepts and Theorems Examples: 1. (PMO 1984-85) Let the rectangle ABCD be such that AB = CD = 4 units and BC = AD = 3 units. A perpendicular is dropped to the diagonal BD from each of the vertices A and C , and let the feet of these perpendiculars be P and Q , respectively. Find PQ . 2. (PMO 1988-89, Modified) The base of a triangle is 15 cm. Two line segments are drawn parallel to the base, terminating in the other two sides, and dividing the triangle into three equal areas. Find the lengths of these two parallel segments. 3. (PMO 1984-85, Modified) A circle is inscribed in a square of side 8 cm. Inside one of the corner spaces between the circle and the square, the largest possible circle is drawn. Find the radius of this smaller circle. 4. A triangle has sides that measure 13, 14 and 15. A line perpendicular to the side of measure 14 divides the interior of the triangle into two regions (one is a triangle and the other is a quadrilateral) of equal areas. What is the measure of the segment of the perpendicular that
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