Question

4) (Assume AR is tangent)Given: AR 12SR - 7.7Find: cs (Round to nearest tenth.)​

Answer 1

The length of CS is 11.0

Explanation:

Given that the length of the tangent AR is 12

The length of SR is 7.7

To find: The length of CS

The tangent secant theorem states that "if a tangent and a secant are drawn from an external point to a circle, then the square of the measure of the tangent is equal to the product of the measures of the secant’s external part and the entire secant."

Applying the tangent secant theorem, we have,

$AR^2=SR\times RC$

Rewriting the above equation, we get,

$AR^2=SR(SR+SC)$

Substituting the values, we get,

$12^2=7.7(7.7+CS)$

Simplifying, we have,

$144=59.29+7.7CS$

Subtracting both sides by 59.29, we get,

$84.71=7.7CS$

Dividing both sides by 7.7, we have,

$11.0013=CS$

Rounding off to the nearest tenth, we get,

$11.0=CS$

Thus, the length of CS is 11.0