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505-555 (Easy)|   Geometry|      
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Sajjad1994
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If J and K are points in a plane and J lies inside the circle C with c 03 Feb 2017, 04:46
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15% (low)

Question Stats:

85% (01:14) correct 15% (01:13) wrong based on 94 sessions

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If J and K are points in a plane and J lies inside the circle C with center O and radius 4, does K lie inside circle C?

(1) The length of line segment JK is 1
(2) The length of line segment OJ is 2.5
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C
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Bunuel
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If J and K are points in a plane and J lies inside the circle C with c 03 Feb 2017, 04:50
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SajjadAhmad
If J and K are points in a plane and J lies inside the circle C with center O and radius 4, does K lie inside circle C?

(1) The length of line segment JK is 1
(2) The length of line segment OJ is 2.5
Show more

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Hope it helps.
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If J and K are points in a plane and J lies inside the circle C with c 03 Feb 2017, 05:00
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SajjadAhmad
If J and K are points in a plane and J lies inside the circle C with center O and radius 4, does K lie inside circle C?

(1) The length of line segment JK is 1
(2) The length of line segment OJ is 2.5
Show more


St I
JK = 1, for this there are 2 possibilities,
a. Both J and K are inside the circle
b. Only J is inside the circle. (see image - part 1)

St I is insufficient

St II
OJ = 2.5 - this gives no information about K
St II is insufficient

Combining both statements we can deduce that K lies inside the circle (see image - part 2)
Since OJ = 2.5 and JK = 1, point K will always be inside the circle with Radius = 4

Hence Option C is correct.
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If J and K are points in a plane and J lies inside the circle C with c 27 Jan 2021, 06:05
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If J and K are points in a plane and J lies inside the circle C with center O and radius 4, does K lie inside circle C?

(1) The length of line segment JK is 1
(2) The length of line segment OJ is 2.5
Show more
Solution:

Statement One Alone:

The length of line segment JK is 1.

We can’t determine whether K lies inside circle C or not based on the information given. For example, if J is very close to O, then K is inside the circle. However, if J is very close to the circumference of circle O, then K could be outside the circle. Statement one alone is not sufficient.

Statement Two Alone:

The length of line segment OJ is 2.5.

Since this doesn’t tell us anything about K, statement two alone is not sufficient.

Statements One and Two Together:

With the information from both statements, we see that line segment OK is no longer than JK + OJ = 1 + 2.5 = 3.5 (note: OK = 3.5 if points O, J and K are collinear; otherwise, OK < 3.5). Since the radius of circle C is 4, this means K must lie inside the circle. Both statements together are sufficient.

Answer: C
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