# What is the length of ST?

Jun 5, 2018

$S T = \sqrt{210} \approx 14.49$ inches

#### Explanation:

By tangent-secant theorem , we have

$\text{(T angent)"^2="(Whole Secant)}$$\times \text{(External Secant)}$

$i . e . T {S}^{2} = T Q \times T R$

Tangent $= T S$

Whole Secant $= T Q = = T R + R Q = 7 + 23 = 30$ inches

External Secant $= T R = 7$ inches

$\rightarrow S {T}^{2} = R T \times Q T$

toST=sqrt(RTxxQT

$\rightarrow S T = \sqrt{7 \times 30} = \sqrt{210} \approx 14.49$ inches