Isosceles Triangle ABC is inscribed in a circle with radius 12cm. Aide AB is a diameter. Determine the perimeter of the triangle, correct to one decimal place.
math - drwls, Monday, July 27, 2009 at 1:52am
Point C must be midway between A and B on the circle since the triangle is isosceles. ABC therefore has angles of 45, 90 and 45 degrees. AB has length 12 cm. AC and BC have lengths
6/sin45 = 6*2/sqrt2 = 6 sqrt2
The total perimeter is 12 + 12sqrt2 =
12(1 + sqrt2)= 29.0 cm
Drawing the figure yourself should help explain where I got the above numbers.