1) Find the distance from the center of a circle to a chord \(30\) inches long, if the diameter of the circle is \(34\) inches.
3) Two circles intersect and have a common chord \(32\) inches long. The centers of the circles are \(42\) inches apart. If the radius of the first circle is \(20\) inches, what is the radius of the second circle?
4) Two circles of radii \(41\) cm and \(15\) cm intersect and have a common chord. If the centers of the two circles are \(52\) centimeters apart, then find the length of the chord.
4) Two circles of radii \(41\) cm and \(15\) cm intersect and have a common chord. If the centers of the two circles are \(52\) centimeters apart, then find the length of the chord.
8) Two circles with an external common tangent have radii of length \(10\) and \(14\). If the distance between the centers of the circles is \(50\), how long is the external tangent segment?
9) Two circles share an external tangent that is \(38\) m in length; the distance between the centers of the circles is \(40\) m. If the radius of the larger circle is \(12\sqrt3\) m, then find the radius of the smaller circle.
10) Two circles with a common internal tangent have radii of length \(11\) and \(17\). If the distance between the centers of the circles is \(36\), how long is the internal tangent segment?
11) Two circles share a common internal tangent that is \(36\)m in length; the distance between the centers of the circles is \(39\) m. If the radius of the smaller circle is \(6\) m, then find the radius of the larger circle.
12) Two circles with an external common tangent of length \(8\) have radii of length \(1\) and \(7\). Find the distance between the centers and the length of the common internal tangent.
9) Two circles share an external tangent that is \(38\) m in length; the distance between the centers of the circles is \(40\) m. If the radius of the larger circle is \(12\sqrt3\) m, then find the radius of the smaller circle.
10) Two circles with a common internal tangent have radii of length \(11\) and \(17\). If the distance between the centers of the circles is \(36\), how long is the internal tangent segment?
11) Two circles share a common internal tangent that is \(36\)m in length; the distance between the centers of the circles is \(39\) m. If the radius of the smaller circle is \(6\) m, then find the radius of the larger circle.
12) Two circles with an external common tangent of length \(8\) have radii of length \(1\) and \(7\). Find the distance between the centers and the length of the common internal tangent.
24) Circle \(T\) is has a center at \((2, 3)\) with a radius of \(5\) units is externally tangent to \(\bigodot H\) that has a center at \((14, 8)\). Find the equation of the common internal tangent.
26) \(\bigodot O\) is inscribed in \(\triangle ABC\) and is externally tangent to \(\bigodot P\). \(\overline{AB}\) and \(\overline{BC}\) are common external tangents to the two circles. If \(AC = 4\) and \(CB = 3\), then calculate the radius of each circle.