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In the diagram above, AB = 10 is the diameter of the circle, and AC =

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In the diagram above, AB = 10 is the diameter of the circle, and AC =  [#permalink]

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23 Oct 2018, 20:45
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Difficulty:

55% (hard)

Question Stats:

48% (01:59) correct 52% (01:38) wrong based on 23 sessions

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In the diagram above, AB = 10 is the diameter of the circle, and AC = 6. Given that point C is inside the circle, which could be the length of BC?

I. 7
II. 8
III. 9

A. I
B. II
C. III
D. I & II
E. II & III

Attachment:

triangle in circle.JPG [ 11.71 KiB | Viewed 277 times ]

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In the diagram above, AB = 10 is the diameter of the circle, and AC =  [#permalink]

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23 Oct 2018, 20:53
3
Bunuel wrote:

In the diagram above, AB = 10 is the diameter of the circle, and AC = 6. Given that point C is inside the circle, which could be the length of BC?

I. 7
II. 8
III. 9

A. I
B. II
C. III
D. I & II
E. II & III

Attachment:
triangle in circle.JPG

Here we can think of three properties

1) Sum of any two sides of the triangle > Third side
i.e. 16>BC >4

2) Angle drawn at circumference in a semicircle is a right angle
But here C is not on circumference i.e. ACB is an Obtuse angle triangle

3) For any obtuse triangle $$c^2 > a^2 + b^2$$ where c is the longest side of triangle

i.e. $$b^2 < 10^2 - 6^2$$
i.e. $$b^2 < 100 - 36$$
i.e. $$b^2 < 64$$
i.e. $$b< 8$$

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In the diagram above, AB = 10 is the diameter of the circle, and AC = &nbs [#permalink] 23 Oct 2018, 20:53
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