# The radius of the circle is 30. Find the value of the obtuse inscribed angle resting on the chord, equal to 30√2.

August 17, 2021 | education

| From the center of the circle, point O, we construct the radii OA and OB.

AOB triangle is isosceles with sides 30 cm and base 30 * √2 cm.

By the cosine theorem, we define the cosine of the angle AOB

AB ^ 2 = ОА ^ 2 + ОВ ^ 2 – 2 * ОА * ОВ * CosАВ

180 = 90 + 90 – 2 * 900 * CosAOB.

2 * 90 * CosAOB = 180 – 180 = 0.

CosAOB = 0.

Angle AOB = 90.

Then the degree measure of the small arc AB is equal to 90, and the large arc AB = (360 – 90) = 270.

Then the inscribed angle ADB = 270/2 = 135.

Answer: The angle is 1350.

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