Question

I HAVE MY MOCKS TOMORROW AND I WILL DO THE SAME TEST THAT I HAVE KNOW HEEEEELP

Answer 1

Answer:

$p=\frac{4\sqrt{10}}{5}$  

Step-by-step explanation:

step 1

Find the radius of the circle

Remember that AB is a tangent to the circle at point B

so

AB is perpendicular to OA

The radius of the circle is equal to the segment OA

In the right triangle OAB

$sin(30\°)=\frac{OA}{OB}$

$OA=(OB)sin(30\°)$

substitute the values

$OA=(16)0.5=8\ units$

step 2

Find the value of p

In the right triangle OPQ

see the attached figure to better understand the problem

Applying the Pythagoras Theorem

$OP^2=OQ^2+PQ^2$

substitute the values

Remember that OP is the radius

$8^2=p^2+(3p)^2$

$64=p^2+9p^2$

$64=10p^2$

$p^2=\frac{64}{10}$

$p=\frac{8}{\sqrt{10}}$

simplify

$p=\frac{4\sqrt{10}}{5}$