Math CentralQuandaries & Queries


Question from Jerry:

Points A and C lie on the circumference of a circle. B is a point inside the circle. When produced, AB and CB meet the circumference at points E and D respectively. Prove that AB = CB, then EB = BD.

Hi Jerry. I can get you started on the proof. Start by connecting C to A and E to D.

Statement   Reason
CB = AB   Given.
mABC = mEBD   Opposite angles of intersecting lines are congruent.
mDCA = mDEA   All inscribed angles subtending the same arc (in this case arc AD) are equal.
ABC is similar
to EBD
  Angle-Angle similarity.


Hope this helps,
Stephen La Rocque.

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