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 finding point of intersection between circle and line

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my answers 

a1:(10,12)

a2: r=7

b:25

c is what i struggle with, so far i worked out the equation for line MN and found the perpendicular bisector line.

i have sketched my progress so far on desmos https://www.desmos.com/calculator/i0vbehvizi

i think i should be able to find point P if i find the intersection between new line and circle by subbing in my equation into the circle but i got x=98 as my answer 

please help thanks.

 Jan 4, 2019
edited by YEEEEEET  Jan 4, 2019

Best Answer 

 #1
avatar+6248 
+3

I'd use the fact that lines tangent to the circle are perpendicular to the radius.

So NPM is a right triangle.

 

\(|MN|^2 = r^2 + |NP|^2\\ 25^2 - 49 = |NP|^2\\ 576 = |NP|^2 \\ |NP| = 24\)

 Jan 4, 2019

2+0 Answers

 #1
avatar+6248 
+3
Best Answer

I'd use the fact that lines tangent to the circle are perpendicular to the radius.

So NPM is a right triangle.

 

\(|MN|^2 = r^2 + |NP|^2\\ 25^2 - 49 = |NP|^2\\ 576 = |NP|^2 \\ |NP| = 24\)

Rom Jan 4, 2019
 #2
avatar+845 
+1

thanks!

YEEEEEET  Jan 5, 2019

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