Quick question about theorems?

Eoin_Sheehy

Ok so for higher level do we have to be able to prove "If a line passes through a point t, then the line is a tangent to the circle at t."

Indiego

Not that I know of :L
I cant find it in my book, and Ive never come across it in exam questions :L

rainaa

we have to know that oneee
i have it anyway.

Colm!

In short, no. In long-form, these are the ten theorems that you can be asked for the JC.

EDIT: This might be on the Project Maths course, I'm not entirely sure. I'll let someone else clarify. It wasn't on my maths course last year. These are what I did last year:

: Vertically opposite angles are equal in measure
: The measures of the three angles of a triangle are equal in measure
: An exterior angle of a triangle equals the sum of the two interior opposite angles in measure
: If two sides of a triangle are equal in measure, then the angles opposite these sides are equal in measure.
: Opposite sides and opposite angles of a parallelogram are respectively equal in measure
: A diagonal bisects the area of a parallelogram
: The measure of the angle at the centre of the circle is twice the measure of the angle at the circumference, standing on the same arc
: A line through the centre of a circle perpendicular to a chord bisects the chord.
: If two triangles are equiangular, the lengths of corresponding sides are in proportion
: In a right-angled triangle, the square of the length of the side opposite to the right angle is equal to the sum of the squares of the lengths of the other two sides

Eoin_Sheehy

Yep, you see it's not included in the list of theorems which can be examined in my exam papers yet in texts and tests normally says that you don't need to learn it with the other that aren't examined but they said nothing about that with this one.

spurious

From the syllabus (and it's the syllabus that is important, not any textbook):

Theorem: If a line passes through a point t on a circle and is
perpendicular to the diameter at t, then the line is a tangent to
the circle at t.

It needs to be known but does not need to be proved.

The syllabus is here

The ones that the proofs need to be known are marked with an asterisk and it is not.

FatRat

If the circle theorem of twice the size of the angle above when on the same arc, that one. If that comes up, do we have to do out the deductions?

Slow Show

I'm gonna go mad here and ask 'what's a tangent?'. It's come up before but I was never really sure what it was, and now is probably the time to find out...

Colm!

Slow Show wrote: »

I'm gonna go mad here and ask 'what's a tangent?'. It's come up before but I was never really sure what it was, and now is probably the time to find out...

A tangent is a line that passes through a circle at one specific point only. That point is usually called 't'

MS PAINT EXPLANATION