In this problem we have a secant to the circle and a tangent to the circle from a common point such that the chord cut off by the secant is the same length as the tangent from the point. Then we look at the ratios of selected lengths along the secant.

1. P is a point on the secant AB of a circle such that the tangent PT which touches the circle at T is the same length as chord AB. Find point C on AB by taking an arc with center at P and passing through T.

a.Constructthe configuration with GSP and present the argument that your construction satisfies the description without resorting to measuring.Click

HEREto see a construction.Click

HEREfor a GSP file.

b. Find the following ratios:

REVIEW OF THE GEOMETRY OF SECANTS AND TANGENTS? YES NO

Reference:

Huntley, H. E. (1970).

. New York: Dover Publications, Inc. (pp. 42 - 43)The Divine Proportion: A Study in Mathematical Beauty

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