The angle at the apex of an isosceles triangle is 140 degrees. The side is 5 cm. Find the radius of the circumscribed circle.

| March 16, 2021 | education

From the top of the obtuse angle B, we draw the height BH, which, in an isosceles triangle, also has a bisector and a median. Then the angle ABН = ABC / 2 = 140/2 = 700. Angle BAH = 180 – 90 – 70 = 20.

AH = CH = AC / 2.

In a right-angled triangle ABН CosBAH = AH / AB.

AH = AB * Cos20 = 5 * Cos20.

The inscribed angle ABC = 140, then the large arc AC = 140 * 2 = 280, and the arc ABC is then equal to 360 – 280 = 80.

The central angle AOC rests on the arc ABC and is equal to its degree measure. Angle AOC = 80, and angle AOH = AOC / 2 = 80/2 = 40, angle OAН = 180 – 90 – 40 = 50.

Then, in a right-angled triangle, AOН CosOAH = AH / AO.

AO = AH / CosOAN = 5 * Cos20 / Cos50 = 5 * 0.94 / 0.64 = 7.34 cm.

Answer: The radius of the circumscribed circle is 7.34 cm.



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