Questions [Circle Geometry] (1 Viewer)

[FriedRice07]

Questions [Circle Geometry] [SOLVED]

Question 1)

LM and FG are two chords of the circle at right angles to each other, and they intersect at P. From P, a line perpendicular to GM is drawn, meeting it at S. SP is produced to meet LF at T.

a) Show that ∆ LTP is isosceles.
b) Show that T is the midpoint of LF.

Question 2)

Two circles touch internally at a point A and the smaller of the two circles passes through O, the centre of the larger circle. AB is any chord of the larger circle, cutting the smaller circle at S. The tangents to the larger circle at A and B meet at a point T.

Prove:
a) AB is bisected at S.
b) O, S and T are collinear.

Question 3

In the above diagram, ABC is a triangle inscribed in a circle. The perpendicular from A onto BC meets it at D and is then produced to meet the circumference at K. The perpendicular from C onto AB meets it at F and is then produced to meet the circumference at G. The two perpendiculars AD and CF meet at the point H.

a) Show that the quadrilaterals AFDC and BFHD are both cyclic.
b) Prove that AB bisects the angle GBH.
c) Prove that GB = BK.

Any help would be appreciated

 

[FriedRice07]

Sorry about the wrong section

I just realised it after i had clicked post.

Thanks for the help

 

[vds700]

this isn't mx2, but anyway:

what??? Circle geo is in the harder 3 unit topics of extension 2

 

[FriedRice07]

@vds700: 3 Unit Mathematics is Extension 1 fyi . :wave:

 

[lyounamu]

@vds700: 3 Unit Mathematics is Extension 1 fyi . :wave:

But harder 3 Unit Mathematics is part of 4 Unit Course.

And that's what he is referring to.

 

[FriedRice07]

But harder 3 Unit Mathematics is part of 4 Unit Course.

And that's what he is referring to.

Oh oh i see