Idiot\'s Guides Basic Math and Pre-Algebra

Chapter 15: Circles 207

A

T

B

D

C

If the chord you drew happened to be a diameter, both intercepted arcs would be 180r, so both
angles would be 90r. That means that a diameter drawn to the point of tangency is perpendicular
to the tangent line, and because a radius is half the diameter, a radius drawn to the point of
tangency is perpendicular to the tangent.

P

O

CHECK POINT

11. Two tangents PA and PE meet at point P outside circle O and touch the circle
    at A and E. Minor arc AE measures 140r and major arc ATE measures 220r. Find
    the measure of ’APE.


12. Two lines pass through point A, outside circle O. One intersects circle O at
    points E and F. The other line intersects the circle at S and then T. The measure
    of ES is 12r and the measure of FT is 52r. Find the measure of ’FAT.


13. Tangent RT touches circle O at point A and meets chord AC. Minor arc AC
    measures 72r. If m’RAC > m’TAC, find the measure of ’RAC.


14. Tangent PQ and secant PRS form an angle of 15r. If arc QS measures 160r, find
    the measure of arc QR.


15. Tangents PA and PB touch circle O at points A and B, dividing the circle into
    two arcs. The measure of the larger arc is twice that of the smaller arc. Find the
    measure of ’P.