The length of segment XY is 52 units and the length of segment HD is 26 units
How to determine the lengths?
Secant lines (a)
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
Secant lines (b)
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
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