An isosceles triangle ABC with base AC equal to 10 m is inscribed in a circle centered O. The height BH is 1 m. Find the radius of the circle if the angle B is obtuse.
Since, by condition, triangle ABC is isosceles, then its height BH is also its median, then AH = CH = AC / 2 = 10/2 = 5 cm.
Let the radius of the circle be equal to X cm.Then the length of the segment OH = OB – BH = (X – 1) cm.
In a right-angled triangle AOH, we apply the Pythagorean theorem.
OA ^ 2 = OH ^ 2 + AH ^ 2.
X ^ 2 = (X – 1) ^ 2 + 25.
X ^ 2 = X ^ 2 – 2 * X + 1 + 25.
2 * X = 26.
X = OA = R = 26/2 = 13 cm.
Answer: The radius of the circle is 13 cm.
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