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Q.1. If in a triangle then angle C is π/k, the numerical quantity k must be
Ans. 3
will simplify to
a^{2} + b^{2} c^{2} = ab
⇒ cos C = 1/2 ⇒ c = 60^{o}
Q.2. If b + c = 3a, then cot B/2 cot C/2 must be equal to
Ans. 2
Q.3. If in a ΔABC, a/cosA = b/cosB, then k sin A cos B = sin C. Where k is equal to . .
Ans. 2
or sin A cos B = cos A sin B
or 2sin A cos B = cos A sin B + sin A cosB = sin (A + B) = sin C
Q.4. In a triangle ABC, side AB = 20, AC = 11, BC = 13, then the diameter of the semicircle inscribed in triangle ABC, whose diameter lies on AB and is touching AC and BC is ___
Ans. 11
CT_{1} = CT_{2} = x
AB = 20
AC = 11
BC = 13
In ΔABC sinA = 3/5 and sinB = 33/65 also
⇒ r = 11/2
Q.5. A cyclic quadrilateral ABCD of area 3√3/4 is inscribed in a unit circle. If one of its sides AB = 1 and the diagonal BD = √3 then find the sum of all its sides.
Ans. 4
By sine rule AB = 1
4.
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