SOLUTION: An isosceles triangle ABC has it vertices on a circle. If length |AB|= 13 and length |BC| = 13 and length |AC| = 10, Calculate
a. The length BM of the triangle
B. The radius of
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Question 1183727: An isosceles triangle ABC has it vertices on a circle. If length |AB|= 13 and length |BC| = 13 and length |AC| = 10, Calculate
a. The length BM of the triangle
B. The radius of the circle to the nearest whole cm
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!
The statement of the problem is deficient, in that there is no definition of point M.
For the problem to make sense, I will assume M is the midpoint of AC.
A nitpicker could also claim that the problem is unsolvable because the given lengths do not specify centimeters....
When an isosceles triangle is inscribed in a circle, the diameter of the circle from the vertex angle of the triangle divides the triangle into two congruent right triangles. In this example, each of those right triangles has hypotenuse 13 and one leg 10/2=5; the Pythagorean Theorem makes the other leg 12.
Let O be the center of the circle, let r be the radius, and look at triangle AMO. AM=5; AO is r, and OM is BM-BO = 12-r. Then
ANSWERS:
a. BM = 12
b. r=169/24 = 7 to the nearest whole cm
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