ABC is a right angled triangle right angled at A such that AB 6 c...........

Quantitative Aptitude (CDS) Geometry

ABC is a right-angled triangle, right-angled at A such that AB = 6 cm and AC = 8 cm. What is the perimeter of the square inscribed in the triangle ABC with maximum area ?

This questions was previously asked in

2024 CDS -1 MATH

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4.5π

3π

3.5π

4π

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Explanation:

Correct option 4: 4π

Given:
∠A = 90°
AB = 6 cm
AC = 8 cm
Concept used:
Inradius of Right angle triangle = (P + B - H)/24
Perimeter of a circle = 2πr
Calculation:
According to the diagram,
BC² = 36+ 64
=BC² = 100
=BC = 10
So Radius = (8+ 6-10)/2
⇒2
Perimeter of the circle = 2π x 2
- The perimeter of the circle is 4π