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555-605 (Medium)|   Geometry|      
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Bunuel
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If the lines shown in the picture touch the circle only at points A an 13 Sep 2018, 05:14
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71% (01:16) correct 29% (01:22) wrong based on 101 sessions

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If the lines shown in the picture touch the circle only at points A and B, what is the maximum distance between C and any point on the circle?

(1) The radius of the circle is 5 units.
(2) The distance between A and C is 9 units.

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If the lines shown in the picture touch the circle only at points A an 20 Sep 2018, 10:09
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Bunuel

If the lines shown in the picture touch the circle only at points A and B, what is the maximum distance between C and any point on the circle?

(1) The radius of the circle is 5 units.
(2) The distance between A and C is 9 units.

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For this problem, we draw a prependicular from tangent CA to the center of the circle,
Then we will have a right triangle.from this we can find the lenght of CO(point C to O(center)).

now substract radius from the lenght and we will have our answer.

Option A and B both are required to find the lenght.

C
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If the lines shown in the picture touch the circle only at points A an 26 Sep 2018, 03:37
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chetan2u The maximum distance between ANY POINT on the circle and C must be twice of radius plus distance between C and P where P is the point on circle while joining C and O. Am I right with this ?

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If the lines shown in the picture touch the circle only at points A an 26 Sep 2018, 03:49
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Shank18
chetan2u The maximum distance between ANY POINT on the circle and C must be twice of radius plus distance between C and P where P is the point on circle while joining C and O. Am I right with this ?

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Yes you are right..
Because we know AC and AO, we will know CO..add the radius and we can get our answer..
\(\sqrt{9^2+5^2}\)+5
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If the lines shown in the picture touch the circle only at points A an 26 Sep 2018, 04:02
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chetan2u
Shank18
chetan2u The maximum distance between ANY POINT on the circle and C must be twice of radius plus distance between C and P where P is the point on circle while joining C and O. Am I right with this ?

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Yes you are right..
Because we know AC and AO, we will know CO..add the radius and we can get our answer..
\(\sqrt{9^2+5^2}\)+5
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Hi chetan2u,

I am unable to get this question!

It says maximum distance, so it has to be either A or B cos they intersect the circle at one point.

First statement gives u Radius but you are not sure cos length of hypotenuse can be anything not necessarily 13(5-12-13 triangle).
Insuff.

Second says
AC =9 units but we know nothing about CB.
Insuff.

Now, taking them together,
Radius=5, AC=9 cms, therefore, Hypotenuse=SQRT(81+25)=SQRT(106)=10.Something

But we still dont know anything about B.

what if point C is positioned more towards B or A.

Values wont be same, so we wont be able to answer the question the MAXIMUM distance between C and either A or B.

So both are insuff. thus E

I hope i was able to explain my doubt!

Looking forward to your explanation. chetan2u
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If the lines shown in the picture touch the circle only at points A an 26 Sep 2018, 04:26
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Bunuel

If the lines shown in the picture touch the circle only at points A and B, what is the maximum distance between C and any point on the circle?

(1) The radius of the circle is 5 units.
(2) The distance between A and C is 9 units.

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honneeey,
Some info on the figure..
1) C makes tangent at A and B and will be at equidistant from A and B, so AC=BC
2) when you join a tangent with centre it makes 90° angle, so here AO will make 90° with AC ... So ACO is a right angled triangle
3) when you draw a bisector of angle BCA, it will pass through centre O and will be the longest distance.. so CD will be the longest distance..

Statement I..
This gives us radius. But we do not know CO
Insufficient
Statement II
This gives us AC, but we do not know radius.

Combined..
Triangle ACO... CO^2=AC^2+AO^2=√(9^2+5^2)=√104
Now CD=CO+OD=(√104)+5
Suff
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