Annoying question

Annoying little question which my aths teacher ealier said he couldnt figure out how to prove. I've just spent a while doing it to find that I can't do it, so here's putting it to you.

N.B. Might actually be impossible and be a mistake on the print out? I don't think it will be though because it looks straightforward enough!

Reply 1

habosh

13

erm I guess as yc is a tangent to the circle then the angle oyc is 90 so it forms a right angle triangle there is a pythagoras therom that the line from the right angle to the mid of the hypotenuse equals half the hypotenuse or sometheing like that check it from the internet though to be sure

Reply 2

GarethBrown

OP

2

As in this image? This is a prrof since it is a general case, correct for any values of a b and c yeah?

Reply 3

Morbo

17

The reason is YTC is an isosceles triangle.

This can be shown by dropping a perpendicular from T to the line YC, hitting it at a point P. Now CPT and CYO are similar triangles, and it follows that YTC is an isosceles triangle, hence YT = CT.

Your maths teacher needs a slap.

Reply 4

GarethBrown

OP

2

He said that noone in the maths department could figure it out, which says a lot really :wink:

Edit. Duh.

Reply 5

habosh

13

Worzo

The reason is YTC is an isosceles triangle.

This can be shown by dropping a perpendicular from T to the line YC, hitting it at a point P. Now CPT and CYO are similar triangles, and it follows that YTC is an isosceles triangle, hence YT = CT.

Your maths teacher needs a slap.

so what I've said is wrong!? :frown:

Reply 6

Morbo

17

habosh

so what I've said is wrong!? :frown:

Well I don't really understand. Did you say "the length of the line from the right-angle vertex to the midpoint of the hypotenuse is half the length of the hypotenuse"?

It would seem that this is true, and so I don't think what you have said it wrong, no. However, it did not answer the question. The question asked for a geometrical reason why the two lengths were equal. The geometrical reason is that they are the two equal lengths of an isosceles triangle. There may well be an algebraic proof given by a theorem, but this was not required.

Reply 7

Morbo

17

GarethBrown

He said that noone in the maths department could figure it out, which says a lot really :wink:

Edit. Duh.

Well, you can educate your maths department.

Reply 8

SsEe

13

CYO is a right angle. So Y lies on the circumference of the circle with diameter OC. T is the midpoint of the diameter so is the centre of the circle. YT and CT are radii so have the same length.
Basically what habosh said only using circle rules instead of pythagoras.

Annoying question

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