Mathematics, 21.08.2019 08:00 chrisraptorofficial

Me with it.
in the figure given below , ab and ac are two chords of a circle of center o and radius r. if ab= 2 ac and the perpendiculars drawn from the center on these chords are of lengths 'a' and 'b' respectively. prove that 4b^2= a^2+3r^2
this question is related to lesson circles

Me with it.in the figure given below , ab and ac are two chords of a circle of cen

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Answer from: Gladistshiala267

OK. I did it. Now let's see if I can go through it without
getting too complicated.

I think the key to the whole thing is this fact:

   A radius drawn perpendicular to a chord bisects the chord.

That tells us several things:

-- OM bisects AB.
   'M' is the midpoint of AB.
   AM is half of AB.

-- ON bisects AC.
'N' is the midpoint of AC.
   AN is half of AC.

-- Since AC is half of AB,
   AN is half of AM.
   a = b/2

Now look at the right triangle inside the rectangle.
'r' is the hypotenuse, so

      a² + b² = r²

But a = b/2, so   (b/2)² + b² = r²

(b/2)² = b²/4        b²/4   + b² = r²

Multiply each side by 4:   b² + 4b² = 4r²
   - - - - - - - - - - -
      0 + 5b² = 4r²
Repeat the
original equation: a² + b² = r²

Subtract the last
two equations: -a² + 4b² = 3r²

Add a² to each side: 4b² = a² + 3r² . <=== ! ! !

Answer from: Quest

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1

Answer from: Quest

if you need just tell me and i will come to the rescue.

step-by-step explanation:

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in the figure given below , ab and ac are two chords of a circle of center o and ra...

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