Question

The circumcircle of a circle circumscribing an equilateral triangle is $24\pi$ units. Find the area of circle inscribed in the equilateral triangle.​

Answer 1

Answer:

Hello

Here is the answer-

Refers to the attachment for the Question,

Circumference of the Circle = 24 × (22/7)

    2 × π × r = 24 × (22/7)

    2r × (22/7) = 24 × (22/7)

     ⇒ 2r = 24

    ⇒ r = 12 cm.

We know, the Side of the Equilateral Triangles inscribed in a circle of radius r = √3 × r

= √3 × 12

= 12√3 cm.

Now, From the Attachment,

We know, OA is Perpendicular on the QR.

[∵ The line drawn from the center to the chord is always Perpendicular]

From the Figure, we can see that OA is the Radius of the Circle.

AR = (1/2)QR 

[∵ The Perpendicular Drawn from the Centre bisects the Chords]

⇒ AR = 6√3 cm.

In Δ OAR,

Applying Pythagoras theorem,

  OR² = OA² + AR²

⇒ (12)² = OA² + (6√3)²

⇒ 144 = OA² + 108

⇒ OA² = 144 - 108

⇒ OA² = 36

⇒ OA = 6 cm.

∴ Area of the Circle = π × r²

  = (22/7) × (6)²

  = 792/7 cm²

∴ the Area of the In circle is 792/7 cm². 

Hope it helps.

Answer 2

Answer:

hope it is helpful to you..