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# Integer Answer Type Questions: Properties of triangle - Notes | Study All Types of Questions for JEE - JEE

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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
a2 + b2- c2 = ab

⇒ cos C = 1/2 ⇒ c = 60o

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
CT1 = CT2 = 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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