Question

Solve for x. Show your work.

Answer 1

5(5+x) = 6(6+4)
25+5x = 60
5x = 35
x = 7

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3(3+5) = 4(4+x)
24 = 16 + 4x
4x = 24-16
4x = 8
x = 2

Answer 2

(i) x=7

(ii) x=2

Explanation:

We are given two secant intersect externally at point P.

Theorem: If two secant intersect outside circle, then the product of the lengths of the segments of one secant is equal to the product of the lengths of the other secant.

Please see the attachment for figure and theorem.

According to theorem,

`AP* BP = CP* DP`

For first diagram:

AP=x+5, BP=5 , CP=10, DP=6

`(x+5)* 5=10* 6`

`x+5=12`

`x=7`

Hence, The value of x is 7

For Second diagram:

AP=8, BP=3 , CP=x+4, DP=4

`8* 3=4* (x+4)`

`x+4=6`

`x=2`

Hence, The value of x is 2