Select the correct answer. In the given figure, m = 118°, m = 76°, and m∠BAC = 35°. Which statement is true? Figure not drawn to scale A. The measure of is 48°, and triangle BCD is isosceles. B. The measure of is 83°, and triangle BCD is isosceles. C. The measure of is 48°, and triangle BCD is not isosceles. D. The measure of is 83°, and triangle BCD is not isosceles.

A circle is a round-shaped figure with all the points on one plane, the distance between the center and all the points on the circumference is the same.

Thre arc mBC inscribes angle BDC

According to the theorem, the angle made by the arc on the center is double that made at the circumference.

mBDC = (1/2) * mBC

mBDC = (1/2) * 118 = 59°

It is also known from the secant theorem that, the angle made by the two secants is equal to half of the angle inscribing the arc.

mA = (1/2) * (mBC - mDE)

35 = (1/2) * (118 - mDE)

70 = 118 - mDE

The measure of DE = 48°

The sum of all the arcs in a circle is 360°

So,

mBC + mCD + mDE + mBE = 360

mCD = 360 - 118 - 48 - 76 = 118°

The angle CBD is inscribed by the arc mCD

mCBD = (1/2) * mCD = (1/2) * 118 = 59°

The angles CBD and BDC are equal, so the triangle is isosceles.

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