Question

Given: AB tangent to circle O at B, and secant through point A intersect the circle at points C and D. Find CD, if

Answer 1

Answer:

CD = 6 cm.

Step-by-step explanation:

In the figure attached AB is the tangent of circle O at point B. A secant through point A intersect the circle at C and D.

mAB = 4cm and  mAC = 2cm

We have find the length of CD.

By the theorem of secant and tangent

AB² = AC×AD

Here AC = 2 cm

and AD = AC + CD = (2 + CD)

Now we replace the values in the formula

4² = 2(2 + CD)

16 = 4 + 2.CD

2.CD = 16 - 4 = 12

$CD=\frac{12}{2}=6$

Therefore CD = 6 cm is the answer.

Answer 2

Answer:

6 cm

Step-by-step explanation:

If you use Tangent-secant product (chapter reference), AB/AC = AD/AB so 4/2 = AD/4. AD = 8, CD = AD - AC = 8 - 2 = 6 cm.