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1960 AMC 12 Question 32

AMC12 · 1960 AMC 12

Question 32

In this figure the center of the circle is $O.$ $\overline{AB}\perp\overline{BC},$ $ADOE$ is a straight line, $\overline{AP}=\overline{AD},$ and $\overline{AB}$ has a length twice the radius. Then:

Question illustration
  1. $\overline{AP}^{\,2}=\overline{PB}\cdot\overline{AB}$
  2. $\overline{AP}\cdot\overline{DO}=\overline{PB}\cdot\overline{AD}$
  3. $\overline{AB}^{\,2}=\overline{AD}\cdot\overline{DE}$
  4. $\overline{AB}\cdot\overline{AD}=\overline{OB}\cdot\overline{AO}$
  5. none of these