ciurcle geo qn (1 Viewer)

[bos1234]

Center is O - forgot to label it






What reason do I give to say that <ROT = <SOT



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The question is <POR = < POS. Prove PQ perpendicular to RS and bisect arc RQs

 

[watatank]

whats the question?

 

[bos1234]

hmm i typed the quesstion but its not coming

What reason do i give to say that < ROT = < SOT

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this is the real question

< POR = < POS
PRove PQ perp. RS and bisects arc RQS

 

[SoulSearcher]

PQ is a straight line, right?

Then < ROT + < POR = 180
and < SOT + < POS = 180

Therefore < ROT + < POR = < SOT + < POS
But since < POR = < POS, then < ROT = < SOT

Should be easy from there.

 

[watatank]

hmm i typed the quesstion but its not coming

What reason do i give to say that < ROT = < SOT

-------------

this is the real question

< POR = < POS
PRove PQ perp. RS and bisects arc RQS

Ok since

< POR + < ROT = 180* (angle sum of a straight is 180*)

Similarly < POS + < SOT = 180*

But < POR = < POS (given) so < ROT = < SOT

There's no real reasons that need to be given, its just a sylogism (sp)
Like saying A > B ..... B > C ... it logically follows that A > C


Ok consider Triangles ROT and SOT

OT is common
< ROT = < SOT (previous proof)
RO = SO (equal radii)

congurent through two sides and inc. angle being respectively equal.

therefore <ROT = <STO (corresponding angles = on cong. tri)

but
<ROT + <STO = 180* (angle sum of straight)

If 2
<ROT = 180*

<ROT = 90*

PQ perpendicular to RS

Next part:

< ROT = < SOT

arcRQ = arcRS (equal arcs subtend equal angles at the centre)

therefore it bisects RQS

Hope that helps :wave:

 

[bos1234]

alright

thanks got it now!!!!!!!!!!