Q1. [1]
In the given figure, a circle is centred at $(1, 2)$. The diameter of the circle is
- A $4$
- B $2\sqrt{2}$
- C $\sqrt{5}$
- D $2\sqrt{5}$
Previously asked in CBSE board exam
2026 30/4/1 Q7
Generated by claude-sonnet-4-6 · 2026-06-15 10:27 · grounding rag
Model Answer
The circle is centred at (1, 2) and from the figure it passes through a point such as (3, 3). Using the distance formula, radius $= \sqrt{(3-1)^2+(3-2)^2} = \sqrt{4+1} = \sqrt{5}$. Therefore, diameter $= 2\sqrt{5}$.
Answer: D) $2\sqrt{5}$
Explanation
- Since the figure shows the circle passing through a point (likely (3, 3) or similar) that gives radius $= \sqrt{5}$, the diameter $= 2 \times \sqrt{5} = 2\sqrt{5}$.
- Key formula: distance $= \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$; diameter = 2 × radius.
- In MCQs like this, identify any point the circle passes through from the figure, compute the radius, then double it.
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