GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 21 Oct 2019, 23:25

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Point A lies on a circle whose center is

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Manager
Joined: 23 Feb 2017
Posts: 58
Point A lies on a circle whose center is  [#permalink]

### Show Tags

05 Jan 2018, 09:41
1
3
00:00

Difficulty:

85% (hard)

Question Stats:

37% (01:57) correct 63% (01:57) wrong based on 61 sessions

### HideShow timer Statistics

Point A lies on a circle whose center is at point C. Does point B lie inside the circle?

1) $$BC^2 = AC^2 + AB^2$$
2) ∠CAB is greater than ∠ABC

_________________
+1 Kudos if you find it helpful.
Math Expert
Joined: 02 Sep 2009
Posts: 58398
Point A lies on a circle whose center is  [#permalink]

### Show Tags

05 Jan 2018, 10:19
1
Point A lies on a circle whose center is at point C. Does point B lie inside the circle?

(1) $$BC^2 = AC^2 + AB^2$$.

This statement implies that triangle ABC is right angled at A (BC being hypotenuse) So, AB is perpendicular to AC, which is radius (AB is tangent to the circle). Thus, B is outside the circle. Sufficient.

Little technicality here: this statement to be sufficient it should be mentioned that A and B are different points. I'm assuming it's given

(2) ∠CAB is greater than ∠ABC.

Larger side of a triangle is opposite larger angle. Hence, this statement implies that BC is larger than AC (radius). Thus, B is outside the circle. Sufficient.

We could use the same logic also for (1): BC (hypotenuse) is larger than AC (radius). Thus, B is outside the circle. Sufficient.

Answer: D.

Hope it's clear.

Attachment:

Untitled.png [ 4.49 KiB | Viewed 651 times ]

Attachment:

Untitled1.png [ 4.85 KiB | Viewed 594 times ]

_________________
Point A lies on a circle whose center is   [#permalink] 05 Jan 2018, 10:19
Display posts from previous: Sort by

# Point A lies on a circle whose center is

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne