91Ó°ÊÓ

Show that if two chords of a circle bisect each other, the chords are diameters and the angles formed are central angles.

Two chords intersect in the interior of a circle, thus determining two segments in each chord. Show that the product of the length of the segments of one chord equals the product of the lengths of the segments of the other chord.

An arch is built in the form of an arc of a circle and is subtended by a chord \(30 \mathrm{ft}\). long. If a chord \(17 \mathrm{ft}\). long subtends half that arc, what is the radius of the circle?

Given: Two concentric circles with center \(\mathrm{O} ;\) chord \(\underline{\mathrm{BC}}\) is a subset of chord \(\underline{A D}\). Prove: \(\underline{A B} \cong \underline{C D}\). (Hint: Draw a perpendicular from \(\mathrm{O}\) to \(\underline{\mathrm{BC}}\).)