Need help with circle geometry! (1 Viewer)

[s_bilgrami89]

I'm stuck on these and could really use some help
http://www.boardofstudies.nsw.edu.au/hsc_exams/hsc2000exams/hsc00_maths/96MAT3U.PDF -
Question 2c

http://www.facebook.com/l.php?u=htt.../hsc00_maths/00mathematics34U.pdf&h=TAQADdds5
Question 5a

http://www.facebook.com/l.php?u=htt.../hsc00_maths/00mathematics34U.pdf&h=TAQADdds5
Question 6a

http://www.facebook.com/l.php?u=htt...0_Mathematics_Extension_1_HSC.pdf&h=TAQADdds5
Last 3 questions in the section on circle geometry

Would really appreciate any help at all, cheers in advance.

 

[UnrealAnchovies]

2(c). (i) SO = OP (radii first circle)

OP = SP (radii second circle)

:. SO = SP = OP

:. SOP is equilateral

(ii) By the same principle (you'd show some working or explanation), TOP is also an equilateral triangle.

:. SOT = SOP + TOP

= pi/3 + pi/3

=2pi/3

(iii) A = 2 x STP

i.e. A = 2 x (Area of sector OSTP - Area of triangle OST)

You should be able to finish that off.

 

[UnrealAnchovies]

5(a) (i) TPA = PBA (angle between a tangent and a chord is equal to the angle in the opp. seg.)

also TPA = PCB (alternate angles in parallel lines)

:. PBA = PCB

(ii) Taking triangles PBA and PBC,

PBA = PCB (part (i))

APB = CPB (common)

:. Triangle PBA ||| Triangle PBC

So by similar triangles, PB/ PA = PC/ PB (you can pretty much fudge this even if you don't know similar triangles facts)

:. PB^2 = PA x PC

 

[UnrealAnchovies]

6(a) and the first one from the circle geo section look too long for this late in the night.

For the second one from the list:

Aim: prove QP = QR

Proof: SQP = SPQ (given)

SQP = QPR (alternate angles in parallel lines)

SPQ = SQP = QRP (angle between tangent and chord is equal to the angle in opposite segment)

:. QRP = QPR

:. QP = QR (equal sides opposite equal angles)



For the third one:

Aim: prove XY is parallel to BC

Proof: ABC = ACB = (lets say) x (given)

BAC = 180 - 2x (angle sum of a triangle)

Now, CAY = ABC = x (angle between tangent and chord equal to angle in opp seg)

For XY to be parallel to BC, we can prove either alternate angles or cointerior angles. I've set it up for cointerior. So,

CAY + BAC + ABC must equal 180 for them to be cointerior

i.e. x + 180 - 2x + x = 180

180 = 180

:. XY is parallel to BC


If there's a mistake anywhere in my working, I blame the time.