Question

I need help!

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

Answer 1

I hope this helps you

Answer 2

`DA=3`

Step-by-step explanation:

We have been given an image of a circle and we are told that Secant DB intersects secant DZ at point D.

We will use intersecting secants theorem to solve our given problem.

Intersecting secants theorem states that if two secants say MN and KL intersect at a point 'X' outside the circle, then product of XN and MX equals the product of XL and KX.

Using intersecting secants theorem we can set an equation as:

`DA\cdot DB=DY\cdot DZ`

Upon substituting our given values in above equation we will get,

`3x\cdot (3x+8)=x\cdot (32+x)`

Upon dividing both sides of our equation by x we will get,

`(3x\cdot (3x+8))/(x)=(x\cdot (32+x))/(x)`

`3\cdot (3x+8)=32+x`

Upon using distributive property
`a(b+c)=a*b+a*c` we will get,

`9x+24=32+x`

`9x-x+24-24=32-24+x-x`

`8x=8`

Upon dividing both sides of our equation by 8 we will get,

`(8x)/(8)=(8)/(8)`

`x=1`

Since the length of DA is 3x, so upon multiplying 3 by 1 we will get,

`\text{Length of DA}=3\cdot 1=3`

Therefore, the length of DA is 3 units.