The Inscribed Quadrilateral

Strategies and Hints

  1. Any triangle inscribed in a semicircle is a right triangle.

    The two right triangles needed for the solution are ADB and ADC.

  1. From the Pythagorean Theorem, segment BD = = 24 cm.
    segment AC = = 15cm.

  2. Since CD = 20 and BD = 24, knowing the cosine of BDC would allow you to use tne Law of Cosines to find BC.

  3. cosine BDC = cos (ADC - ADB)  
                     = (cos ADC) (cos ADB) +
                        (sin ADC) (sin ADB)

Solution

Using the formula in the fourth hint, the cosine of BDC = .

The Law of Cosines then gives for BC. So, BC = 8.8 cm.