Geometry Review, Part II

  1. Given triangle DAC inscribed in semicircle , as shown below, the central angle is twice the angle .

To prove this, we use the fact that is a right angle and the fact that the angles in any triangle sum to .

Summing the angles in triangle BDC, we get , or .

Since triangle ADB is isosceles (two of its legs are radii of the circle), the missing angle must be equal to .

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Neal Carothers -