Question

Describe the relationship among the lengths of the segments formed by the two secants. You may use words and/or an equation.
Suppose CG=4 in., CH=5 in. and GE=6 in. Is it possible to find the length of DH? If so, show how to find the length. If not, explain why not.

Answer 1

It is possible to find DH based on the stated theorem

Secant-secant rule:

This rule states that if two secants are drawn from an external point to a circle, then the product of the measures of one secant's external part and that entire secant is equal to the product of the measures of the other secant's external part and that entire secant.

Mathematically:

• (CG+GE)CG = (CH+HD)CH

Given the following parameters

CG=4 in

CH=5 in

GE=6 in

Substitute to check if we can find DH

(4+6)*4 = (5+DH)*5

10*4 = 25 + 5DH

40 - 25 = 5DH

15 = 5DH
DH = 3in

Therefore it is possible to find DH based on the stated theorem

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