CDS 2026 · PYQ · Geometry / Inscribed Circle · medium
A Question is given followed by two Statements I and II. Consider the Question and the Statements and mark the correct option.
Question: A circle is inscribed in the equilateral triangle Δ. What is the radius of the circle?
Statement-I: Area of Δ is equal to 16√3 cm².
Statement-II: Perimeter of Δ is 24 cm.
A.The Question can be answered by using one of the statements alone, but cannot be answered using the other statement alone
B.The Question can be answered by using either Statement alone✓ Correct
C.The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone
D.The Question cannot be answered even by using both the Statements together
Explanation
For an equilateral triangle, knowing area alone gives side: (√3/4)s² = 16√3 → s² = 64 → s = 8, then inradius r = s/(2√3) = 8/(2√3). Knowing perimeter alone also gives side: 3s = 24 → s = 8, then r = 8/(2√3). Each statement alone is sufficient. So either statement alone can answer the question.
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