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Properties of Triangle Test - 14

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Properties of Triangle Test - 14
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    If α β, are the acute angles of an obtuse angled triangle, then tan α tan β is
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    If R and r are the radii of the circumcircle and incircle of a regular polygon of n sides, each side being of length a, then a is equal to
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    In a triangle ABC, if c = (a - b) sec θ, then tan θ is equal to
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    If the angles of a triangle are in the ratio 1 : 3 : 5 and θ denotes the smallest angle, then the ratio of the largest side to the smallest side of the triangle is
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    In a cyclic quadrilateral ABCD; a, b, c, d denote the length of the sides AB, BC,CD and DA respectively. Then cos A is equal to
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    The angles of a triangle ABC are in A.P. The largest is twice the smallest and the median to the largest side divides the angle at the vertex in the ratio 2 : 3. If the length of the median is 2√3 cm, then the length of the largest side is
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