IM2.7 T9: A special inscribed (?) angle
Construction Task
1. Construct a circle with center A through point B.[br]2. Construct point C (≠B) on the circumference of the circle.[br]3. Construct chord BC so that BC is NOT a diameter.[br]4. Construct a tangent line [icon]/images/ggb/toolbar/mode_tangent.png[/icon]through point B.[br]5. You should have a big arc and a small arc on your circle now. On the small arc, construct point D, segments BD and CD, and angle BDC.[br]6. Construct point E on the tangent line on the side of the big arc, and use it to measure angle CBE.[br]
1. What kind of angle is BDC?[br]2. Move point D, and describe what happens to angle BDC. Why do you think this is true?[br]3. What is the relationship between angles BDC and DBE? Why do you think this is true? (Hint: what happens when you slide D close to B?)[br]4. Summarize what you've learned in your best academic language. What is the relationship between an angle formed by a chord and a tangent, and the arc it opens onto?
Find angles a, b, and c.