Question

What is the value of d to the nearest tenth?

26.5

29.3

33.8

14.3

Answer 1

Option A. d = 26.5

Explanation:

If two secants are drawn to a circle from an external point of the circle then the product of one secant (length) and its external part is equal to the product of other secant and its external part.

By this theorem

22 × (22 + 40) = 26 × ( 26 + d )

22 (62) = 26 × (26 + d)

`(1364)/(26)` = 26 + d

52.5 = 26 + d

d = 52.5 - 26 = 26.5

Option A. d = 26.5 is the answer.

Answer 2

Answer: First option is correct.

Explanation:

Since we have given that

PA = 22

PB = 22+40=62

PC = 26

PD = 26+d

As we know the rule of tangents :

PA.PB=PC.PD

`22* 62=26(26+d)\\\\1364=676+26d\\\\1364-676=26d\\\\688=26d\\\\(688)/(26)=d\\\\d=26.46\\\\d=26.5`

Hence, First option is correct.