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# A triangle and a circle lie in the same plane. Is this circle the

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Retired Moderator
Joined: 22 Aug 2013
Posts: 1428
Location: India
A triangle and a circle lie in the same plane. Is this circle the  [#permalink]

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17 Jan 2019, 22:00
2
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Difficulty:

35% (medium)

Question Stats:

62% (01:03) correct 38% (01:10) wrong based on 56 sessions

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A triangle and a circle lie in the same plane. Is this circle the incircle of the triangle?

(1) The triangle and the circle intersect in less than 5 distinct points.

(2) The triangle and the circle intersect in more than 3 distinct points.
Math Expert
Joined: 02 Aug 2009
Posts: 7991
Re: A triangle and a circle lie in the same plane. Is this circle the  [#permalink]

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19 Jan 2019, 19:43
amanvermagmat wrote:
A triangle and a circle lie in the same plane. Is this circle the incircle of the triangle?

(1) The triangle and the circle intersect in less than 5 distinct points.

(2) The triangle and the circle intersect in more than 3 distinct points.

The question talks of incircle and then intersecting point, so the incircle is supposed to have all three sides as tangent .
Thus, any incircle will have 3 intersection points.

Now, 3 intersection points are a must property but not sufficient in itself.
It may well be possible that the circle intersects one side at 2 places and the second at one. But it does not touch the thirs at all.

Statement I gives 3 as an option. So, answer can be yes or No. Insufficient

statement II negates the possibility of 3 touches only. Thus it is NOT an incircle. Sufficient

B
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Re: A triangle and a circle lie in the same plane. Is this circle the   [#permalink] 19 Jan 2019, 19:43
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