Suggested languages for you:

Americas

Europe

Problem 373

In circle \(\mathrm{O}\), diameter \(\underline{\mathrm{AB}}\) is extended to point \(\mathrm{C}\). Line \(\underline{\mathrm{CF}}\) intersects the circle at points \(D\) and \(E .\) If \(D C \cong \underline{O E}\) show that $\mathrm{m} \angle \mathrm{EOA}\( is three times as large as \)\mathrm{m} \angle \mathrm{ACE}\(. [Hint; Draw radius \)\underline{\mathrm{OD}}]$.

Expert verified

In summary, by drawing radius $\overline{OD}$ and applying the Inscribed Angle and Central Angle Theorem, as well as the Triangle Sum Theorem and Exterior Angle Theorem, we have established that the measure of angle EOA is three times as large as the measure of angle ACE, or \(\mathrm{m} \angle \mathrm{EOA} = 3 \mathrm{m} \angle \mathrm{ACE}\).

What do you think about this solution?

We value your feedback to improve our textbook solutions.

- Access over 3 million high quality textbook solutions
- Access our popular flashcard, quiz, mock-exam and notes features
- Access our smart AI features to upgrade your learning

Chapter 19

If perpendiculars from the ends of a diameter of any circle are drawn to a tangent of that circle, prove that the sum of the lengths of the perpendiculars is equal to the length of the diameter.

Chapter 19

Line segment \(\underline{\mathrm{CD}}\) is the diameter of circle \(\mathrm{O}\), as seen in the diagram, and \(\underline{A D}\) is tangent to the same circle. Given that \(\underline{A B C}\) is a straight line, prove that $\triangle A B D\( and \)\Delta D B C$ are mutually equiangular.

Chapter 19

\(\underline{E B A}\) and \(\underline{E G D}\) are secants of \(\odot P\). Chords \(\underline{A F}\) intersects \(\underline{E G D}\) at point \(G\). If $E B=5, B A=7, E C=4, G D=3\(, and \)A G\( \)=6\(, find \)\mathrm{GF}$

Chapter 19

Prove that the measure of the angle formed by a tangent and a chord of a circle is one-half the measure of its intercepted arc.

Chapter 19

If \(\mathrm{P}\) and \(\mathrm{Q}\) are points on the circumference of two concentric circles, prove that the angle included between the tangents at \(\mathrm{P}\) and \(\mathrm{Q}\) is congruent to that subtended at the center by \(\underline{P Q}\).

The first learning app that truly has everything you need to ace your exams in one place.

- Flashcards & Quizzes
- AI Study Assistant
- Smart Note-Taking
- Mock-Exams
- Study Planner