2026 · Q71
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 IArea of Δ is equal to 16√3 cm².
Statement IIPerimeter of Δ is 24 cm.
Which one of the following is correct in respect of the above Question and the Statements?
Elementary MathematicsGeometry: Lines, Angles and Triangles
- AThe Question can be answered by using one of the statements alone, but cannot be answered using the other statement alone
- BThe Question can be answered by using either Statement alone
- CThe Question can be answered by using both the Statements together, but cannot be answered using either Statement alone
- DThe Question cannot be answered even by using both the Statements together
Explanation
For an equilateral triangle the inradius is r=s√3/6. Statement I gives s=8 from area 16√3=(√3/4)s²; statement II gives s=8 from perimeter 24. Each statement alone determines r, option B.