Latest Maths Olympiad Aptitude Question SOLUTION: Find all integers a, b, c, d satisfying the following relations: (i) 1 a b c d; (ii) ab + cd = a + b + c + d + 3.

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Previous Question: The circumference of a circle is divided into eight arcs by a convex quadrilateral ABCD, with four arcs lying inside the quadrilateral and the remaining four lying outside it. The lengths of the arcs lying inside the quadrilateral are denoted by p, q, r, s in counter-clockwise direction starting from some arc. Suppose p + r = q + s. Prove that ABCD is a cyclic quadrilateral. Next Question: Let ABC be a triangle in which AB = AC and \CAB = 90◦. Suppose M and N are points on the hypotenuse BC such that BM2 + CN2 = MN2. Prove that \MAN = 45◦.

(#M40021964) MATHS OLYMPIAD question ALGEBRA Keep an EYE

Find all integers a, b, c, d satisfying the following relations:
(i) 1 a b c d;
(ii) ab + cd = a + b + c + d + 3.: Asked In Maths Olympiad MAN (10 years ago); Unsolved; Is this Puzzle helpful? (0) (0) Submit Your Solution

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Previous Question: The circumference of a circle is divided into eight arcs by a convex quadrilateral ABCD, with four arcs lying inside the quadrilateral and the remaining four lying outside it. The lengths of the arcs lying inside the quadrilateral are denoted by p, q, r, s in counter-clockwise direction starting from some arc. Suppose p + r = q + s. Prove that ABCD is a cyclic quadrilateral. Next Question: Let ABC be a triangle in which AB = AC and \CAB = 90◦. Suppose M and N are points on the hypotenuse BC such that BM2 + CN2 = MN2. Prove that \MAN = 45◦.

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