NCERT · Class 10 · Mathematics · Areas Related to CirclesIf the sum of the areas of two circles with radii $R1$ and $R2$ is equal to the area of a circle of radius $R$, then:
Step-by-Step Solution
Area of circle 1 is $\pi R_1^2$, area of circle 2 is $\pi R_2^2$, and area of large circle is $\pi R^2$. Given $\pi R_1^2 + \pi R_2^2 = \pi R^2$, dividing by $\pi$ gives $R_1^2 + R_2^2 = R^2$.
Detailed Options Breakdown
Option : R_1 + R_2 = R
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Areas Related to Circles.
Option 1: R_1^2 + R_2^2 = R^2 (Correct Answer)
Correct choice. Refer to the step-by-step verified solution guidelines above for details.
Option 2: R_1 + R_2 > R
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Areas Related to Circles.
Option 3: R_1^2 - R_2^2 = R^2
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Areas Related to Circles.
💡 Study Guide: This question tests core syllabus concepts from Areas Related to Circles. For formulas, key summaries, and mock exam reference guides, read the full Areas Related to Circles Revision Notes.