The figure below shows an equilateral triangle (∆ABC) tangent to circle O at three points. If the perimeter of ∆ABC is 18, the area of circle O = : Crackverbal Support

The figure below shows an equilateral triangle (∆ABC) tangent to circle O at three points. If the perimeter of ∆ABC is 18, the area of circle O = Print

Modified on: Tue, 12 Oct, 2021 at 2:10 PM

CONCEPT: The question tests the basics of Mensuration and Geometry

SOLUTION:

The in-radius of an equilateral triangle is √3 * (side) /6
(In-radius is 1/3 the length of an altitude, because each altitude is also a median of the triangle)

Perimeter of the given triangle =18 units
=>Each side of the triangle =18/3 = 6units [Equilateral triangle]
In radius = √3 * (6) / 6 =√3

Hence area = π r^2
=π *√3 * √3
=3π (OPTION D)

Did you find it helpful? Yes No

Help Desk Software by Freshdesk

The figure below shows an equilateral triangle (∆ABC) tangent to circle O at three points. If the perimeter of ∆ABC is 18, the area of circle O = Print

Related Articles