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Subject: "geometry"     Previous Topic | Next Topic
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Conferences The CTK Exchange High school Topic #363
Reading Topic #363
Dovid
Member since Aug-6-04
 Apr-18-07, 11:35 PM (EST)
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"geometry"
 
   Given a circle x² + y² = 25 and point C(6, -8). From C two tangents are drawn to the circle at A and B. Find the length of chord AB,

Now the center is at the origin and the radius is 5. OA (the radius) is perpendicular to AC and OB (radius is perpendicular) to BC.

AC = BC; triangle OAB is isosceles.

What next?

(When I drew this on graph paper, I estimated AB to 8, and the altitude from O to chord AB is 3).

Peace!


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alexbadmin
Charter Member
1987 posts		 Apr-18-07, 11:52 PM (EST)
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1. "RE: geometry"
In response to message #0
 
   Observe that CO = 10 and, by the Pythagorean theorem, in the right triangle OAC angle at C is π/6. This means that ΔABC is equilateral. Finf the length of the tangent (AC or BC). AB is equal to that number.


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Dovid
Member since Aug-6-04
 Apr-19-07, 09:19 AM (EST)
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2. "RE: geometry"
In response to message #1
 
   >Observe that CO = 10 and, by the Pythagorean theorem, in the
>right triangle OAC angle at C is š/6. This means that
>ÄABC is equilateral. Finf the length of the tangent
>(AC or BC). AB is equal to that number.

I'm lost: Why is Co=10?

Thanks.

Peace!


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Dovid
guest
 Apr-19-07, 09:19 AM (EST)
 
3. "RE: geometry"
In response to message #1
 
   Please forget my question of how you get CO=10. I just realized the answer.

Thank you for your patience.


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alexbadmin
Charter Member
1987 posts		 Apr-19-07, 09:21 AM (EST)
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4. "RE: geometry"
In response to message #1
 
   >right triangle OAC angle at C is š/6.

Looks like the symbol does not consistently come out the same. The angle at C is 30°


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