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can someone help me solve numbers 25 and 27? Thanks you :)

 May 17, 2016

Best Answer 

 #6
avatar+26397 
+5

can someone help me solve numbers 25 and 27? Thanks you :)

 

without mistake:


25.
Isosceles triangle: OAD=ODAExterior Angle Theorem: AOP=OAD+ODAAOP=OAD+OADAOP=2OAD|:2AOP2=OAD412=OAD20.5=OAD

 May 17, 2016
 #1
avatar+118710 
0

25.

 

<POD is 180 degrees,  

<POA=41

so <AOD=139

triangle AOD is isoceles so 

<OAD= 0.5*(180-139)=0.5*41=   20 degrees and 30 minutes

 May 17, 2016
 #2
avatar+118710 
0

27.   Mmm

Well it has to be more than 3 because the two tangents to a circle subtended from a point will be equal.

(I not sure how I should word that) 

I can't be 9 either.  For the same reason.

So it has to be between 3 and 9.

What about 8 ......

No, it'll have to be less than that.

 

OK I don't think it can be any of those but I would like someone to give a more mathematical precise......

 May 17, 2016
 #3
avatar+26397 
+5

can someone help me solve numbers 25 and 27? Thanks you :)

 

25.

Isosceles triangle: OAD=ODAExterior Angle Theorem: OAP=OAD+ODAOAP=OAD+OADOAP=2OAD|:2OAP2=OAD412=OAD20.5=OAD

 

see: https://www.mathsisfun.com/geometry/triangle-exterior-angle-theorem.html

 

27.

Secant-Tangent Rule: x2=3(3+9)x2=312x2=36x=6

 

see: http://www.regentsprep.org/regents/math/geometry/gp14/circlesegments.htm

 

laugh

 May 17, 2016
edited by heureka  May 17, 2016
edited by heureka  May 17, 2016
edited by heureka  May 17, 2016
 #5
avatar+33659 
+5

Well done heureka!  I knew there had to be a simple way - I just didn't know the secant-tangent rule.  Must remember that in future.

Alan  May 17, 2016
 #4
avatar+33659 
+5

I did it as follows:

 

points1

points2

.

 May 17, 2016
 #6
avatar+26397 
+5
Best Answer

can someone help me solve numbers 25 and 27? Thanks you :)

 

without mistake:


25.
Isosceles triangle: OAD=ODAExterior Angle Theorem: AOP=OAD+ODAAOP=OAD+OADAOP=2OAD|:2AOP2=OAD412=OAD20.5=OAD

heureka May 17, 2016
 #8
avatar+118710 
+5

Question 27.

 

I am looking at an alternative to Heureka's and Alan's answers.  

Heureka And Alan did both inspire this answer.    Thanks  guys laugh

 

I cannot remember all theorems relating to circes so I am going to use this more common theorem.

 

The angle between a tangent and a chord is equal to the angle subtended by the chord in the alternate segment.

Proof is here:

https://www.youtube.com/watch?v=LCfgfg8Jv8g

 

Now to find x  laugh

 

Consider   ABDandCBA

<BAD = <BCA   The angle bteween a chord and a tangent is equal to the anle subtended by the chord in the alternate segment    

<ABD = <CBA   Common angle

ABDCBA

 

Now I am going to use the ratios of similar triangles:

 

ABCB=BDBAx12=3xx2=36x=6units

 

 

 Aug 23, 2016

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