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JEE • MATHEMATICS • PROPERTIES OF TRIANGLES

Properties of triangles practice · Hard

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Practice format and chapter quiz

These sets use single-correct-answer MCQs. They do not cover every JEE Main or JEE Advanced question format and are not full-length mock papers.

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1 Hard

1 of 7

Application +4 | -1

a,b,c

are the sides of a tringle, then

\frac{a}{{b + c - a}} + \frac{b}{{c + a - b}} + \frac{c}{{a + b - c}}\;

View answer and explanation

Correct option: B

\ge 3

Option B

\ge 3

is correct because it is derived using the AM-GM inequality after a suitable substitution.

2 Hard

2 of 7

Application +4 | -1

In a

\triangle A B C, \frac{r_1}{b c}+\frac{r_2}{c a}+\frac{r_3}{a b}

is equal to

View answer and explanation

Correct option: D

\frac{1}{r}-\frac{1}{2 R}

Option D (

\frac{1}{r}-\frac{1}{2 R}

) is correct because it is derived by using the formulas for exradii and the inradius of a triangle.

3 Hard

3 of 7

Application +4 | -1

The least perimeter of a cyclic quadrilateral of given area

A

square units is

View answer and explanation

Correct option: D

4\sqrt A

The correct answer is D (

4\sqrt A

) because using AM-GM inequality on the area formula of a cyclic quadrilateral gives the least perimeter.

4 Hard

4 of 7

Application +4 | -1

In the ambiguous case, if

a,\,\,b

and

A

are given and

{c_1},\,{c_2}

are two values of the third side

c

, then

c_1^2 - 2\,{c_1}{c_2}\,\,\cos \,\,2A + c_2^2 = \;

View answer and explanation

Correct option: A

4{a^2}\,\,{\cos ^2}A

Option A (

4{a^2}\,{\cos ^2}A

) is correct because it results from trigonometric identities and algebraic manipulation of the given conditions in the ambiguous case.

5 Hard

5 of 7

Analyzing +4 | -1

There exist a

\Delta \;ABC

satisfying

View answer and explanation

Correct option: D

{\left( {a + b} \right)^2} = {c^2} + ab

and

\sqrt 2 \left( {\sin A + \cos A} \right) = \sqrt 3

Option D (

{\left( {a + b} \right)^2} = {c^2} + ab

and

\sqrt 2 \left( {\sin A + \cos A} \right) = \sqrt 3

) is correct because it is the only option that satisfies the triangle inequality and angle properties.

6 Hard

6 of 7

Analyzing +4 | -1

If in a triangle

ABC,\,\,\cos A\,\,\cos B + \sin A\,\,\sin \,B\,\,\sin C = 1

, then the triangle is

View answer and explanation

Correct option: C

Isosceles right angled

Option C (Isosceles right angled) is correct because by simplifying the given equation, we find that A = B and C = 90°, which means the triangle is isosceles and right-angled.

7 Hard

7 of 7

Application +4 | -1

If the angles

A, B

and

C

of triangle

A B C

are in arithmetic progression and

a, b, c

represents length of sides opposite to angles

A, B

and

C

respectively, then the value of

\frac{a+c}{\sqrt{\left(a^2-a c+c^2\right)}}

is:

View answer and explanation

Correct option: D

2 \cos \frac{A-C}{2}

Option D is correct because using the given conditions and trigonometric identities, the expression simplifies to

2 \cos \frac{{A-C}}{{2}}

Revision notes and key takeaways

Review PROPERTIES OF TRIANGLES in your textbook or class notes, then use this set to check your understanding.

Key Takeaways

✓ This set contains 7 single-correct-answer MCQs on PROPERTIES OF TRIANGLES.
✓ Try each question before opening its answer. Read the explanation where one is available.
✓ Sign in to save submitted answers. Revisit incorrect answers alongside your textbook or class notes.

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Properties of triangles practice · Hard

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