91Ó°ÊÓ

The hands of a clock form a \(120^{\circ}\) angle at \(\underline{?}\) o'clock and at \(\underline{?}\) o'clock.

For each exercise draw a circle and inscribe the polygon in the circle. A parallelogram

Draw \(\odot O\) with perpendicular radii \(\overline{O X}\) and \(\overline{O Y}\). Draw tangents to the circle at \(X\) and \(Y\). a. If the tangents meet at \(Z\), what kind of figure is OXZY? Explain. b. If \(O X=5,\) find \(O Z\)

a. Draw a circle. Place points \(A, B,\) and \(C\) on it in such positions that \(m \overline{A B}+m \overline{B C}\) does not equal \(m \overline{A C}\). b. Does your example in part (a) contradict Postulate \(16 ?\)

For each exercise draw a circle and inscribe the polygon in the circle. An acute isosceles triangle

Sketch a circle with two noncongruent chords: Is the longer chord farther from the center or closer to the center than the shorter chord?

Sketch a circle \(O\) with radius 10 and chord \(\overline{X Y} 8 \mathrm{cm}\) long. How far is the chord from \(O ?\)

For each exercise draw a circle and inscribe the polygon in the circle. A quadrilateral \(P Q R S\). with \(\overline{P R}\) a diameter

Use a compass to draw a large \(\odot O .\) \(\text{Draw a central}\) \(\angle A O B\). a. Label three other points \(P, Q,\) and \(R\) that are on \(\odot O\) but not on \(\widehat{A B}\). Then draw \(\angle A P B, \angle A Q B,\) and \(\angle A R B\) b. Use a protractor to find \(m \angle A O B, \quad m \angle A P B, \quad m \angle A Q B,\) and \(\angle A R B.\) c. What is the relationship between \(m \angle A P B, m \angle A Q B,\) and \(m \angle A R B ?\) What is the relationship between \(m \angle A O B\) and \(m \angle A P B ?\)

For each exercise draw \(\odot O\) with radius \(12 .\) Then draw radii \(\overline{O A}\) and \(\overline{O B}\) to form an angle with the measure named. Find the length of \(\overline{A B}\). $$m \angle A O B=90$$