Math Is Fun Forum

Au101

Member

Registered: 2010-12-01

Posts: 353

The point of intersection of two tangents to a circle

Hello again mathisfun and welcome to fun with circles:

Question 19 in my textbook has me a little bit stuck. It goes like this:

I've done the first part of the question, but on the second part, I get an answer that disagrees with the book's and I'm not sure who's right.

This is what I've done:

.

The gradient of the radius to A is:

Therefore, the equation of the tangent to C at A is:

Therefore, at the point of intersection:

I chose to eliminate y:

Sub x into (2)

But, my textbook has the opposite sign:

So: Who's right? If I'm right - well, that's nice If not: what've I done wrong? Get confused with signs? I wouldn't be too surprised, but I've checked several times!

Bob

Administrator

Registered: 2010-06-20

Posts: 10,643

Re: The point of intersection of two tangents to a circle

hi Au101,

I'm getting your answer.  My sketch had a > b and the tangents crossing on the positive y axis. (if a < b then on the negative).  So the y coordinate has to be positive.  Your answer agrees with this and the book answer puts the point on the negative y axis, so I'm going with your answer. 

C1 is the mirror image of C in the x axis so the book answer is for C1.  Could easily be a typo somewhere.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Au101

Member

Registered: 2010-12-01

Posts: 353

Re: The point of intersection of two tangents to a circle

Thank you bob bundy, I really appreciate it! It can be a bit of a pain when you and the book are the only authorities to consult on your answer

Bob

Administrator

Registered: 2010-06-20

Posts: 10,643

Re: The point of intersection of two tangents to a circle

Yes it can.  But notice what I did to check.  I was going to put in some numbers and construct it, but I realised it was sufficient to consider a>b and a<b to determine which answer was implausible.  For a long time, bobbym had a piece of advice in his signature along those lines ... "check it with numbers" .

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob