Asked by Amy

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.
Answered by drwls
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.
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