Question

Use the figure to answer the questions.

Answer 1

The two secants intersect at an exterior point and their

relationship is given by the intersecting secant theorem.

Correct response:

(a) (CG + GE) × CG = (CH + DH) × CH

(b) Yes, it is possible to find the length of DH

• DH = 3 inches

What is the relationship between the given secants?

(a) According to the intersecting secants theorem, given the

two secants, CE  and CD drawn from the same exterior point

C, where the secant CE has the external segment CG, and

secant CD has the external segment CH.

The relationship between two secants is and their external

segments is presented as follows;

• CE × CG = CD × CH

CE = CG + GE

CD = CH + DH

Therefore;

• (CG + GE) × CG = (CH + DH) × CH

(b) Where; CG = 4 in., CH = 5 in., and GE = 6 in., it is possible to

find the length of DH, given that the number of unknowns in

the equation of the relationship are four, and the values of

three of the variables (CG, CH, and GE) are given, therefore;

• It is possible to, find the length of the fourth variable, DH

The length of DH is given as follows;

Plugging in the values of the variables, gives;

(4 + 6) × 4 = (5 + DH) × 5

10 × 4 = 5² + 5 × DH

5 × DH = 10 × 4 - 5² = 15

$DH = \dfrac{15}{5} = \mathbf{3}$

• DH = 3 inches

Learn more about the intersecting secants theorem here:

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