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Level 9 Geometry / Circle Theorems GCSE Question

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Reply 1
Original post by Retsek
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Draw the line RT on your diagram and think about what circle theorems you can use. Notice that there are tangents in the diagram...

Also think about what you need to show to prove that ST = UT.

When you post questions please provide more information e.g. show your working and explain why you're stuck.
Reply 2
Original post by notnek
Draw the line RT on your diagram and think about what circle theorems you can use. Notice that there are tangents in the diagram...

Also think about what you need to show to prove that ST = UT.

When you post questions please provide more information e.g. show your working and explain why you're stuck.


What I have is:
Angle OTS = 18, because OTP = 90
Angle TSU = 72, exterior angle of pentagon

I need to prove that the triangle TSU is an isosceles by finding a second angle in the triangle aside from TSU.

EDIT: I've got it don't worry
(edited 6 years ago)
Original post by Retsek
What I have is:
Angle OTS = 18, because OTP = 90
Angle TSU = 72, exterior angle of pentagon

I need to prove that the triangle TSU is an isosceles by finding a second angle in the triangle aside from TSU.

EDIT: I've got it don't worry


Hi i've got this same question for homework and i've found all the angles you listed above. How do you find a second angle in the triangle to prove tsu is isosceles
Reply 4
Original post by crisildaj
Hi i've got this same question for homework and i've found all the angles you listed above. How do you find a second angle in the triangle to prove tsu is isosceles

I recommend starting a new thread if you need help with this.
Original post by Notnek
I recommend starting a new thread if you need help with this.


Its fine. Ive got it now.
1) draw line OR and OT;
2) in the new irregular pentagon, ∠ROT=540-108×2-90×2=144;
3) ∠RUT=1/2 of ∠ROT=0.5×144=72;
4) ∠TSU=180-108=72;
5) ∠TSU=∠TUS=72, thus ST=UT.
(edited 6 years ago)
The diagram represents the starting position (AB) and the finishing position (CD) of ladder as slips. The ladder is leaning against a vertical wall. Given: AC=x, OC=4AC,BD=2AC and OB=5m from an equation in x,find x and hence find the length of the ladder
Original post by Mathuskanth
The diagram represents the starting position (AB) and the finishing position (CD) of ladder as slips. The ladder is leaning against a vertical wall. Given: AC=x, OC=4AC,BD=2AC and OB=5m from an equation in x,find x and hence find the length of the ladder


Please start a new thread if you need help with this - don't bump a thread from last year.

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