JEE Main 2023MathematicsProperties of TrianglesHardMCQ

JEE Main 2023 — Properties of Triangles Question with Solution

JEE Main 2023 (01 Feb Shift 1)

Question

For a triangle ABC, the value of cos2A+cos2B+cos2C is least. If its inradius is 3 and incentre is M, then which of the following is NOT correct?

Choose an option

Show full solutionCorrect option: D
Correct answer
Darea of ∆ABC is 2732

Step-by-step explanation

We know that,

cos2A+cos2B+cos2C≥-32

i.e., mincos2A+cos2B+cos2C=-32

So,

cos2A=cos2B=cos2C=-12

⇒A=B=C=60°

So, triangle ABC is an equilateral triangle.

Let the side of triangle be a.

Also,

r=∆s=3

⇒2∆2s=3

⇒234a23a=3

⇒a=183=63

So, perimeter is =3a=183 units.

Area=34a2=813=273 sq. units

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About this question

This is a previous-year question from JEE Main 2023, covering the Properties of Triangles chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.