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Examine the diagrams below. For each one, use the geometric relationships to solve for the given variable.

  1. is tangent to at and
    . What is ?

    Circle, center labeled, C, with points on the circle as follows: Point on upper left  labeled, m, point at bottom, labeled, p, point on bottom right, labeled, Q, & horizontal line, containing point, P, & another point to the right of, P, labeled, R, Segments from, C, to P, & from C, through, Q, to, R, create triangle, C,P,R, Segment, Q,R, labeled, x, & segment P,R, labeled, 5.

  1. radius units

    A circle is drawn with a chord, X. The smaller arc between the endpoints of chord, x, is 102 degrees.

Draw a diagram to help visualize the problem. Right triangle, C,P,R, horizontal leg, P R, labeled, 5, vertical leg, C P, labeled, r, angle, C, labeled theta. hypotenuse, C P, labeled, R, +, x. Point on side, C R, labeled, Q, & segment, Q R, labeled, x.

Added to the triangle, angle c, labeled, 46 degrees.

Draw a diagram to help visualize the problem. Added to circle, segments from the center, to the end points of the chord, with dashed segment from center, perpendicular to the chord, creating 2 right triangles. Each radii labeled, 7 units, each central angle for the right angles, labeled theta.

Angles labeled theta, changed to label, 51 degrees.