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
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 + 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
[tex]DH = \dfrac{15}{5} = \mathbf{3}[/tex]
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