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If AB is the diameter of the circle with center X and C is a point on

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If AB is the diameter of the circle with center X and C is a point on  [#permalink]

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New post 13 Feb 2019, 13:06
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If AB is the diameter of the circle with center X and C is a point on the circle such that AC = AX = 3, what is the perimeter of triangle ABC ?

A. 9 \(\sqrt{3}\)/2

B. 9

C. 6+ 3\(\sqrt{3}\)

D. 9+ 3\(\sqrt{3}\)

E. 9 \(\sqrt{3}\)

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Re: If AB is the diameter of the circle with center X and C is a point on  [#permalink]

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New post 13 Feb 2019, 21:18
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SajjadAhmad wrote:
If AB is the diameter of the circle with center X and C is a point on the circle such that AC = AX = 3, what is the perimeter of triangle ABC ?

A. 9 \(\sqrt{3}\)/2

B. 9

C. 6+ 3\(\sqrt{3}\)

D. 9+ 3\(\sqrt{3}\)

E. 9 \(\sqrt{3}\)


Now ABC is a right angled triangle with C as 90°, because AB is the diameter.
Now AX is radius and equal to 3, so AB = diameter = 6, AC=3..
Thus by Pythagorean theorem BC=√(6^2-3^2)=√(36-9)=√27=3√3..
Perimeter = 3+6+3√3=9+3√3

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If AB is the diameter of the circle with center X and C is a point on  [#permalink]

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New post 14 Feb 2019, 11:30
SajjadAhmad wrote:
If AB is the diameter of the circle with center X and C is a point on the circle such that AC = AX = 3, what is the perimeter of triangle ABC ?

A. 9 \(\sqrt{3}\)/2

B. 9

C. 6+ 3\(\sqrt{3}\)

D. 9+ 3\(\sqrt{3}\)

E. 9 \(\sqrt{3}\)



given AC=CX=3
so CX=3 means radius is 3 so AX= 3 as well and AB = 6 diameter
ABC is a right angled triangle
BC^2= AC^2 + BC ^ 2
36-9 =BC ^2
BC = 3√3
permiter = 6+3+3√3
9+3√3 IMO D
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If AB is the diameter of the circle with center X and C is a point on   [#permalink] 14 Feb 2019, 11:30
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