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Home > GC > Chapter 11 > Lesson 11.2.3 > Problem 11-102


Solve for the variables in each of the diagrams below. Assume that point is the center of the circle in part (b).  

  1. A tangent and a secant, meet outside a circle, creating angle, labeled, 28 degrees.  Angle interior cuts off 2 arcs, smaller labeled, 61 degrees, larger labeled, x. Tangent segment between angle vertex, & point of tangency, labeled, y, Secant divided into 2 segments where intercepted with circle, closest segment labeled, 4, & segment between secant intersections, labeled, 18.

    (ext. sec. seg. + int. sec. seg.)


  1. Circle with center, C, radius labeled, r, and chord labeled, 10. Minor Arc intercepted by chord, labeled 50 degrees. Major arc labeled, z.

    Draw a perpendicular bisector on the chord to the center of the circle, and then create two triangles.

    Added to diagram, line segments from, C, to each end of the chord, and from, C, through, and perpendicular to chord. Left triangle sides labeled, hypotenuse, r, half of chord, 5, and central angle labeled, 25 degrees.

  1. 2 secants, meet outside a circle, each, divided into 2 segments, where intercepted with circle. Segments are labeled, as follows: top: closest to angle, 9, &, a, bottom, closest to angle, 8, &, unknown. A bracket includes both segments, on bottom secant, labeled, 21.

    Draw two intersecting chords, which will create two congruent triangles.

    Added to diagram, Dashed line segments, from first intersection top ray, to second intersection, bottom ray, and from second intersection top ray, to first intersection, bottom ray.