In the circle, AB = 42, BC = 18 and CD = 4. What is the value of x?

Solution:

The external intersecting secant theorem states that if two secants (as shown above) intersect then:

BC × AC = CD × (CD + x) —-- (1)

BC = 18

AB = 42

CD = 4

AC = AB + BC = 42 + 18 = 60

Substituting the values in equation (1) we have

18 × 60 = 4 × (4 + x)

(18 × 60) / 4 = (4 + x)

18 × 15 = 4 + x

270 = 4 + x

x = 270 - 4 = 266

In the circle, AB = 42, BC = 18 and CD = 4. What is the value of x?

Summary:

In the circle, AB = 42, BC = 18 and CD = 4 the value of x is 266