document.write( "Question 1066804: Find the radius of the circle passing through the vertices of a right angled triangle when length of the perpendicular sides are 6 and 8. \n" ); document.write( "

Algebra.Com's Answer #682010 by KMST(5328) $\"\"$ $\"About$

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If a the circle passes through the vertices of a triangle,
\n" ); document.write( "the angles of the triangle are inscribed angles in the circle.
\n" ); document.write( "Inscribed angles intercept an arc whose measure is twice the measure of the inscribed angle.
\n" ); document.write( "in particular, the right angle intercepts half of the circumference,
\n" ); document.write( "meaning that the hypotenuse of the right triangle in this problem
\n" ); document.write( "is the diameter of the circle.
\n" ); document.write( "A right triangle with legs (the perpendicular sides) of length 6 and 8,
\n" ); document.write( "is a 3-4-5 right triangle,
\n" ); document.write( "meaning a scaled up by a factor of $\"2\"$ version
\n" ); document.write( "of a triangle with sides measuring $\"3\"$ , $\"4\"$ , and $\"5\"$ .
\n" ); document.write( "In that scaled-up version,
\n" ); document.write( "the hypotenuse (diameter of the circle) measures $\"2%2A5\"$ , so the radius measures $\"2%2A5%2F2=highlight%285%29\"$ . \n" ); document.write( "

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