Question

Secant DB intersects secant DZ at point D. Find the length of DA

Answer 1

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Answer 2

Answer:

The length of DA is 3 units.

Step-by-step explanation:

Given information: YZ=32, DY=x, DA=3x adn AB=8.

By using intersection secant theorem:

$DY\times DZ=DA\times DB$

$DY\times (DY+YZ)=DA\times (DA+AB)$

$x\times (x+32)=3x\times (3x+8)$

$x^2+32x=9x^2+24x$

$9x^2+24x-x^2-32x=0$

$8x^2-8x=0$

$8x(x-1)=0$

$x=0,x=1$

The value of x can not be zero, therefore the value of x is 1 and the length of DA is

$3x=3\times 1=3$

Therefore the length of DA is 3 units.