91Ó°ÊÓ

In Exercises 3–8, write the standard equation of the circle. (See Example 1.) a circle with center \((0,0)\) and radius 7

The circular stone mound in Ireland called New grange has a diameter of 250 feet. A passage 62 feet long leads toward the center of the mound. Find the perpendicular distance x from the end of the passage to either side of the mound. PICTURES CANNOT COPY

Prove the Segments of Secants Theorem (Theorem 10.19). (Hint: Draw a diagram and add auxiliary line segments to form similar triangles.)

Use the Tangent Line to Circle Theorem (Theorem 10.1) to prove the Segments of Secants and Tangents Theorem (Theorem 10.20) for the special case when the secant segment contains the center of the circle.

Use congruent triangles to prove the Perpendicular Chord Bisector Theorem (Theorem 10.7). Given \(\overline{EG}\) is a diameter of \(\odot L.\) \(\overline{EG} \perp \overline{DF}\) Prove \(\overline{DC} \cong \overline{FC}, DG \cong FG\)

Prove the Segments of Secants and Tangents Theorem (Theorem 10.20). (Hint: Draw a diagram and add auxiliary line segments to form similar triangles.)

PROBLEM SOLVING You are lying in a hot air balloon about 1.2 miles above the ground. Find the measure of the arc that represents the part of Earth you can see. The radius of Earth is about 4000 miles.

CONSTRUCTION Construct an equilateral triangle inscribed in a circle.

Telecommunication towers can be used to transmit cellular phone calls. A graph with units measured in kilometers shows towers at points \((0,0),(0,5),\) and \((6,3)\) . These towers have a range of about 3 kilometers. a Sketch a graph and locate the towers. Are there any locations that may receive calls from more than one tower? Explain your reasoning. b. The center of City \(\mathrm{A}\) is located at \((-2,2.5),\) and the center of City \(\mathrm{B}\) is located at \((5,4)\) . Each city has a radius of 1.5 kilometers. Which city seems to have better cell phone coverage? Explain your reasoning.

CONSTRUCTION The side length of an inscribed regular hexagon is equal to the radius of the circumscribed circle. Use this fact to construct a regular hexagon inscribed in a circle.