The length of segment XY is 52 units and the length of segment HD is 26 units
<h3>How to determine the lengths?</h3>
<u>Secant lines (a)</u>
To do this, we make use of the following intersecting secant theorem
VZ * VW = VY * VX
Substitute the known values in the above equation
12 * 40 = VY * 8
Divide by 8
12 * 5 = VY
Evaluate the product
VY = 60
The length VX is
XY = VY - VX
Substitute the known values in the above equation
XY = 60 - 8
Evaluate
XY = 52
Hence, the length of segment XY is 52 units
<u>Secant lines (b)</u>
To do this, we make use of the following intersecting secant theorem
GH^2 = HC * HD
Substitute the known values in the above equation
13^2 = 6.5 * HD
Divide by 6.5
13^2/6.5 = HD
Evaluate the quotient
26 = HD
The length HD is
HD = 26
Hence, the length of segment HD is 26 units
Read more about secant lines at:
brainly.com/question/25871159
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