Lesson Three circles touching externally
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<H2>Three circles touching externally</H2> <H3>Problem 1</H3>Two circles with centers A and B are touching externally. Third circle with center C touches both the circles A and B externally. Suppose AB = 3cm, BC = 3cm and AC = 4cm. Find the radii of the circles. <B>Solution</B> <pre> When two circles touch externally, the distance between their center is the sum of their radii. It gives you the system of three equations a + b = 3, (1) a + c = 4, (2) b + c = 3. (3) where a, b and c are the radii of the three circles with the centers A, B and C respectively. To solve the system, first add all the three equations. You will get 2a + 2b + 2c = 3 + 4 + 3 = 10, which implies a + b + c = 5. (4) Now extract equation (3) from equation (4) (both sides). You will get a = 5-3 = 2. Extract equation (2) from equation (4) (both sides). You will get b = 5-4 = 1. Finally, extract equation (1) from equation (4) (both sides). You will get a = 5-3 = 2. <U>Answer</U>. 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