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Home > GC > Chapter 12 > Lesson 12.2.4 > Problem 12-92

12-92.

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

  1. is tangent to at and . Find .

A circle is drawn with a line tangent to the circle at point, P. A line C, P, is drawn from the center of the circle to, P. Another point to the right of, P, on the circle is, Q. A line C, Q, is extended outside of the circle to point, R, where it meets the tangent line. Q, R, is labeled, x. There is a triangle C, P R drawn. Another point on the circle to the left of, P, is point, M. The arc, P, M, Q measures 314 degrees.

  1. and intersect at .
    A circle with chords C D, and A B, which intersect at point labeled E, Line segments labeled as follows: E C, & E D, each have 1 tick mark, E B, is 8, & E A, is 18.


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

    Draw out of the chord that has been given.

    Circle with center labeled, c, has chord, labeled x, endpoints of chord are labeled, A, and B, Radii, C A, & C B, each labeled 7, minor arc between points, A & B, labeled 102 degrees.

    According to the Law of Cosines:

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