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State True or False in each of the following statements.
$$r_1$$, $$r_2$$ are the radii of two circles passing through the centres of one another. If $$3r_1 + r_2 = 15$$ then $$r_1$$ is equal to $$\frac{15}{4}$$
Correct Answer: True
Let the distance between the centres be $$d$$. The first circle passes through the second centre, so $$d = r_1$$, and the second passes through the first centre, so $$d = r_2$$. Hence $$r_1 = r_2$$, and $$3r_1 + r_1 = 15$$ gives $$r_1 = \frac{15}{4}$$. The statement is True.
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