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Question
If the area of a circle is equal to sum of the areas of two circles of diameters 10 cm and 24 cm, then the diameter of the larger circle (in cm) is:
Options
A. 34
B. 26
C. 17
D. 14
Solution
Let r1 and r2 be the radii of the two given circles.
Given, 2r1 = 10 cm
∴ r1 = 5 cm
Also, 2r2 = 24 cm
∴ r2 = 12 cm
Let R be the radius of the larger circle.
Given, area of larger circle = Sum of areas of two given circles
`therefore piR^2=pir_1^2+pir_2^2`
`rArr R^2=(5cm)^2+(12cm)^2`
`rArr R^2=25^2+144cm^2`
`rArr R^2=169cm^2`
`rArr R^2=sqrt169cm`
`rArr R^2=13cm`
Thus, the diameter of the larger circle is (2 × 13) cm = 26 cm
Hence, the correct answer is B.
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