Circle Geo Problem (Possibly Hard, possibly easy. Argh) (1 Viewer)

[adzy]

I got a geometry question that looks deviously simple but alas I have not had any success.

Q8 Circle Geometry in 1998 4U past paper

AB is diamater of a circle. A chord RQ is drawn intersecting AB at 45 degrees at P.

Prove AB^2 = 2(PQ^2+PR^2)

Diagram attached.

 

[David_O]

Construct perpendicular from O to QR at P'
PR^2 + PQ^2 = (P'R-PP')^2 + (P'R+PP')^2 = 2r^2 = (1/2)d^2

 

[adzy]

(P'R-PP')^2 + (P'R+PP')^2 = 2r^2

I don't get this step.

 

[David_O]

Expand.
sides op equal angles
Pythag.

 

[adzy]

Oh I see it now. Thanks a lot.

 

[haboozin]

dodgy question:

could we measure it if it doenst say not to scale??

 

[pLuvia]

err.. if it says not to scale then its not to scale, thus the sides are not to the same ratio etc. Measuring it will only waste precious time

 

[haboozin]

err.. if it says not to scale then its not to scale, thus the sides are not to the same ratio etc. Measuring it will only waste precious time

yea, i understand the meaning.

one of the questions was prove length a = length b.

so if they are in the same ratio, they would equal.

it was just, there was a really hard circle geometry question 8 in my trials and it just happened to have not said it, so i just did that. haha i know its so stupid and pretty unfair to the person who can actually figure it out and does not reflect your ability at all in mathematics..

 

[adzy]

At least in Westpac you can construct it (geometry problems) and then measure it and guess the closest possible answer (if care is taken into your construction)

 

[who_loves_maths]

^ what's the highest award you've got for the Wespac Aust. Maths. Comp.s?

 

[adzy]

Prize. But only in years 7/8, then its like High D's for me. And this year I don't think I'll get a prize either. Bleh, ran out of time. Damnit I want my $50.

I did more problem solving in those years, with the extra curricular maths thingoes the school had. Now in the later years, I think the narrow maths HSC syllabus has bogged me down. Sure, that's it, not my gradual dumbening.