Thread: Circle Geometry - five question

Hey guys,

Any help on these questions would be great, they're the only five I couldn't get my head around out of a set of 32!

1) P is a midpoint of a chord AB of a circle. XY is a chord containing the point P. The tangents at X and Y meet AB extended at M and N respectively. Prove that AM = BN.

2) PQ and RS are common tangents to two intersecting circles. If T is one of the points of intersection of the two circles, prove that the circles through T, P, Q and through T, R, S touch each other.

3) ABC is a triangle inscribed in a circle. BE and CF are perpendiculars to AC and AB respectively. AP is drawn perpendicular to EF and, when produced meets the circle at Q. Prove that angle ABQ is a right angle.

4) Draw three circles that intersect the other two. Prove that the three common chords are concurrent.

5) A right angled triangle ABC with right angle at A circumscribes a circle of radius r. Prove that r = 0.5(c + b - a) where a, b, c are the length measures of the sides of the triangle.

Thanks guys!

Originally Posted by AlvinCY

Any help on these questions would be great, they're the only five I couldn't get my head around out of a set of 32!
1) P is a midpoint of a chord AB of a circle. XY is a chord containing the point P. The tangents at X and Y meet AB extended at M and N respectively. Prove that AM = BN.
2) PQ and RS are common tangents to two intersecting circles. If T is one of the points of intersection of the two circles, prove that the circles through T, P, Q and through T, R, S touch each other.
3) ABC is a triangle inscribed in a circle. BE and CF are perpendiculars to AC and AB respectively. AP is drawn perpendicular to EF and, when produced meets the circle at Q. Prove that angle ABQ is a right angle.
4) Draw three circles that intersect the other two. Prove that the three common chords are concurrent.
5) A right angled triangle ABC with right angle at A circumscribes a circle of radius r. Prove that r s= 0.5(c + b - a) where a, b, c are the length measures of the sides of the triangle.

May I ask you, "why should any one of us simply answer any one of these questions"?
If you do get a complete answer, will you use it as your own?

Well.

To be honest, I don't turn to math help form unless I can't do them myself (I do have a maths degree) it's just that sometimes I get stuck on something simple!

And plus, they're not for me, I'm tutoring a kid, and the textbook doesn't provide solutions, which is why I'm going to the effort of working it out for them...

However, I can understand if you choose not to answer any of them!

Originally Posted by AlvinCY

they're not for me, I'm tutoring a kid, and the textbook doesn't provide solutions, which is why I'm going to the effort of working it out for them...

Let me see if I really understand this?
You are being paid as a tutor. You do not understand the subject matter.
So you ask us to bail you out?

I understand the subject matter, but at times I do get stuck on questions. It's not as if I haven't attempted myself. If you do not wish to answer the questions, then fine.

This forum is not restricted to students, and therefore as a tutor, I am still able to post questions.

Anyway, if you wish to delete my thread, then go ahead. But I think that would just be rude and void of the forum's purpose.

I will keep this thread open for now but any further replies, should there be any, must be kept on-topic to the OP.