The intersecting secant theorem states the relationship between the two intersecting secants of the same circle. The given problems can be solved using the intersecting secant theorem.

<h3>What is Intersecting Secant Theorem?</h3>

When two line secants of a circle intersect each other outside the circle, the circle divides the secants into two segments such that the product of the outside segment and the length of the secant are equal to the product of the outside segment other secant and its length.

a(a+b)=c(c+d)

1.)

6(x+6) = 5(5+x+3)

6x + 36 = 25 + 5x + 15

x = 4

2.)

4(2x+4)=5(5+x)

8x + 16 = 25 + 5x

3x = 9

x = 3

3.)

8x(6x+8x) = 7(9+7)

8x(14x) = 112

112x² = 112

x = 1

4.)

(x+3)² = 16(x-3)

x² + 9 + 6x = 16x - 48

x² - 10x - 57 = 0

x = 14.0554

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8 0

2 years ago

How many real does this 2x^2-5x+3=0 equation have

Pavlova-9 [17]

2 $x^{2}$ -5x+3=0

x= $\frac{-(-5)+ \sqrt{(-5) ^{2}-4*2*3 } }{2*2}$

x=3/2;x=1

3 0

3 years ago