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1 answer:
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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
(a) According to the intersecting secants theorem, given the
two secants, CE and CD drawn from the same exterior point
<em>C</em>, 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;
- <u>(CG + GE) × CG = (CH + DH) × CH</u>
(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;
- <u>It is possible to, find the length of the fourth variable, </u><u>DH</u>
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 = <u>3 inches</u>
Learn more about the intersecting secants theorem here:
The intersecting secants theorem says
That is, for either secant line, you take the length of the part of the secant line outside the circle (6 and 5 in this case) and multiply it by the "total" length of the secant line between the point where the two secant lines intersect and the furthest point where the secant touches the circle (6+12=18 and 5+x in this case). The theorem says these products are equal.
Then