Question

Consider the circle where QR = 7 units and UT= 4 units. What is the value of X, if x represents the length of segment ST? A. 15 units B. 8.75 units C. 6 units D. 2.86 units Need help with this problem please!

Answer 1

Option C:

x = 6  units

Solution:

QR = 7 units, RS = 5 units, UT = 4 units and ST = x

If two secants intersect outside a circle, the product of the secant segment and its external segment s equal to the product of the other secant segment and its external segment.

⇒ SR × SQ =  ST × SU

⇒ 5 × (5 + 7) =  x × (x + 4)

⇒ 5 × 12 =  x² + 4x

⇒ 60 =  x² + 4x

Subtract 60 from both sides.

⇒ 0 = x² + 4x - 60

Switch the sides.

⇒ x² + 4x - 60 = 0

Factor this expression, we get

(x - 6)(x + 10) = 0

x - 6 = 0, x + 10 = 0

x = 6, x = -10

Length cannot be in negative measures.

x = 6 units

Option C is the correct answer.