Question

Please help with easy math problem.

What is the value of d to the nearest tenth?

A. 11.2
B. 13.8
C. 16.7
D. 17.5

Answer 1

Option B is correct

d = 13.8

Explanation:

Definition:

If two secant segments are drawn to a circle from the same external point(P),

the product of the length of one secant segment and its external part is equal to product of the length of the other secant segment and its external part.

As per the statement:

Labelled the diagram:

then;

PA = 14 units , AB = 20 units, PC = 16 units and CD = d units

Find PB and PD:

PB = 14+20 = 34 units

PD = 16+d units

then by above definition we have;

`PA \cdot PB = PC \cdot PD`

⇒
`14 \cdot 34 = 16 \cdot (16+d)`

⇒
`476=16 \cdot (16+d)`

Divide both sides by 16 we have;

`29.75 = 16+d`

Subtract 16 from both sides we have;

13.75 = d

or

d = 13.75 units

Therefore, the value of d to the nearest tenth is, 13.8