Discussion

Question:

In the figure given below, ABC is an equilateral triangle. If the area of bigger circle is 1386 cm², then what is the area (in cm²) of smaller circle. [π = 22/7]

Explanation:

Area of larger circle = 1386 = πr²
⇒ r = 21

The larger circle is incircle of triangle ABC.
In circle of an equilateral triangle = a/2√3 = 21
⇒ side of the equilateral triangle ABC = 42√3

Now, let us draw a line DE which is tangent to both the circles. DE will also be parallel to BC.

Now ∆ADE will also be an equilateral triangle.
Height of ∆ADE = Height of ∆ABC - diameter of larger circle
= 42√3 × √3/2 - 42 = 63 - 42 = 21 cm.

∆ADE ≈ ∆ABC
Height of ∆ADE is one-third the height of ∆ABC
∴ Inradius of ∆ADE is one-third the inradius of ∆ABC = 1/3 × 21 = 7 cm.

∴ Area of smaller circle = 22/7 × 7² = 154 cm².

Hence, option (b).

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