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Help plsSolve for [x]. Assume that lines which appear Tangent are Tangent. a) 17b) 4c) 10d) 12

Help plsSolve for [x]. Assume that lines which appear Tangent are Tangent. a) 17b-example-1
User Animesh Kumar Paul
by
3.0k points

1 Answer

26 votes
26 votes

Lines UW and VT are intersecting chords at point K. According to the intersecting chords theorem,

VK * KT = UK * KW

From the diagram,

VK = x + 4

KT = x - 1

UK = 6

KW = 6

Thus,

(x + 4)(x - 1) = 6 * 6

x^2 - x + 4x - 4 = 36

x^2 + 3x - 4 - 36 = 0

x^2 + 3x - 40 = 0

We would solve the quadratic equation by factorisation. We would two terms such that their sum or difference is 3x and their product is - 40x^2. The terms are 8x and - 5x. Thus, we have

x^2 + 8x - 5x - 40 = 0

x(x + 8) - 5(x + 8) = 0

(x + 8) = 0 and (x - 5) = 0

x = - 8 and x = 5

The value for x can only be positive. Thus,

KT = x - 1 = 5 - 1

KT = 4

The correct option is B

User Mrid
by
2.5k points
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