Anonymous
Anonymous asked in Science & MathematicsMathematics · 4 weeks ago

simple geometry question?

A chord of a circle measures 18 meters. A smaller circle concentric with the first is drawn such that it divides the given chord into three equal pieces. The radius of the larger circle is longer than that of the smaller one by 4 meters. What is the radius of the smaller circle?

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  • 4 weeks ago
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    They share a common height, h, from the chord to the center

    h² = r² - 3²

    h² = ( r + 4 )² - 9²

    ( r + 4 )² - 9² =  r² - 3²

    r² + 8r - 65 = r² - 9

    8r = 56

    r = 7

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