Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 03 May 2015, 15:07

### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# In the xy-coordinate system, rectangle ABCD is inscribed

Author Message
TAGS:
Manager
Joined: 13 Apr 2006
Posts: 56
Followers: 0

Kudos [?]: 1 [0], given: 0

In the xy-coordinate system, rectangle ABCD is inscribed [#permalink]  04 May 2006, 08:06
In the xy-coordinate system, rectangle ABCD is inscribed within a circle having the equation x^2 + y^2=2t. Line segment AC is a diagonal of the rectangle and lies on the x-axis. Vertex B lies in quadrant II and vertex D lies in quadrant IV. If side BC lies on line y=3x+15, what is the area of rectangle ABCD?

Can you please help?! A thorough explanation would be great b/c I am totally lost with this.
Intern
Joined: 04 Apr 2006
Posts: 1
Location: India
Followers: 0

Kudos [?]: 0 [0], given: 0

The first thing to notice is that the Circle has its center as (0,0) which makes our job simpler.

Once you have the figure right , you will see that point 'C' is on the x-axis => it is of the form (...,0).

Now, 'C' also lies on the line y = 3x + 15 , so 'C' is ( -5 , 0 )
since 0 = 3(-5) + 15.

This means the radius of our circle is 5 , and so
x^2 + y^2 = 25 = 2t. => t = 12.5

Since 'C' is (-5,0) , 'A' should be (5,0). [ AC lies on the x-axis ].

Now to find 'B' , we substitute , y as 3x + 15 in
the eqn x^2 + y^2 = 25.

x^2 + (3x + 15)^2 = 25 ..solving this , we get
x = -5 or -4 .

Since -5 refers to 'C', then point 'B' must be
( -4 , 3 ). [ we got 3 this way 3 = 3(-4) + 15. ]

So, point B is 3 units above the x-axis. This means,
The triangle ABC has area as
0.5 * base * height = 0.5 * 10 * 3 = 15.

Now, a diagonal divides a rectangle into two equal parts ,

so the area of the rectangle is
2 * 15 = 30 units.
Similar topics Replies Last post
Similar
Topics:
4 Rectangle ABCD is inscribed in circle P. What is the area of 3 21 Oct 2013, 07:36
In the xy-coordinate system, rectangle ABCD is inscribed wit 0 29 Oct 2014, 07:55
11 ABCD is a rectangle inscribed in a circle. If the length of AB is thr 8 16 Apr 2011, 23:04
35 In the xy-coordinate system, rectangle ABCD is inscribed within a circ 22 24 Mar 2011, 21:59
Rectangle ABCD is inscribed in circle C. What is the 5 25 Jun 2008, 02:46
Display posts from previous: Sort by