Unformatted text preview: angles 1 O SE and 1 OC E are congruent (they have same hypotenuse and a leg of equal length, namely, r ), and so they have the same area: 1 2 6 r = 3 r ; also, area (1 O SE ) = 1 2 ra , where a =  CT  . We conclude that 6 + 6 r = 3 r + 3 r + 1 2 ra ; that is, 12 = ra . The Pythagorean theorem (applied to 1 OCT ) gives r 2 + a 2 = ( r + 2 ) 2 = r 2 + 4 r + 4 , and so a 2 = 4 r + 4. Since 12 = ra , we have 144 r 2 = 4 r + 4 , and this simpli f es to r 3 + r 2 − 36 = 0....
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 Fall '11
 KeithCornell
 Pythagorean Theorem, Right triangle, Hypotenuse, triangle

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