Question

2. PT is tangent to circle O and PN intersects circle O at point J. Find the radius of the circle.

Answer 1

@jim_thompson5910
Hey can you help?

Answer 2

@artofspeed

Answer 3

let me think and read this for a moment

Answer 4

okie dokie

Answer 5

Ok it's always best to start off with a drawing

Luckily that's been done for us, so let's just bring it front and center

Answer 6

Now extend line segment PN to get this

Answer 7

now we can use theorem 3 found on this page

http://www.regentsprep.org/Regents/math/geometry/GP14/CircleSegments.htm

to find the length of NQ

Answer 8

Let x = length of NQ

Using theorem 3 we get

b*c = a^2

8*(12+x) = 12^2

96 + 8x = 144

8x = 144 - 96

8x = 48

x = 48/8

x = 6

So NQ is 6 units long

Answer 9

Now extend line segment ON into an infinitely long line like so



this new line intersects the circle at 2 points: R and S