Circle

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shashank.ism: Legendary Member; Posts: 1022; Joined: Mon Jul 20, 2009 11:49 pmFollowed by: 2 members; Location: Gandhinagar; Thanked: 41 times

by shashank.ism » Tue Feb 09, 2010 7:24 am

A circle passes through the vertex C of rectangle ABCD and touches its sides AB and AD at P and Q respectively. If the distance from C to the line segment PQ is equal to 4 units, then the area of the rectangle ABCD in sq. units (is)

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Source: Beat The GMAT — Problem Solving | Tue Feb 09, 2010 7:24 am

ldoolitt: Master | Next Rank: 500 Posts; Posts: 184; Joined: Sat Apr 14, 2007 9:23 am; Location: Madison, WI; Thanked: 17 times

by ldoolitt » Tue Feb 09, 2010 7:35 am

shashank.ism wrote:A circle passes through the vertex C of rectangle ABCD and touches its sides AB and AD at P and Q respectively. If the distance from C to the line segment PQ is equal to 4 units, then the area of the rectangle ABCD in sq. units (is)

20
12
16
greater than 20
none of these

Hmmm, by "touches" do you mean "intersect with once" or "is tangent to"? I've never seen that wording before...

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shashank.ism: Legendary Member; Posts: 1022; Joined: Mon Jul 20, 2009 11:49 pmFollowed by: 2 members; Location: Gandhinagar; Thanked: 41 times

by shashank.ism » Tue Feb 09, 2010 11:22 am

ldoolitt wrote:
shashank.ism wrote:A circle passes through the vertex C of rectangle ABCD and touches its sides AB and AD at P and Q respectively. If the distance from C to the line segment PQ is equal to 4 units, then the area of the rectangle ABCD in sq. units (is)

20
12
16
greater than 20
none of these
Hmmm, by "touches" do you mean "intersect with once" or "is tangent to"? I've never seen that wording before...

touches means obviously the sides of rectangle is tangent to circle Idoolitt. attached figure will surely hep you

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harsh.champ: Legendary Member; Posts: 1132; Joined: Mon Jul 20, 2009 3:38 amFollowed by: 6 members; Location: India; Thanked: 64 times; GMAT Score:760

by harsh.champ » Tue Feb 09, 2010 1:07 pm

ldoolitt wrote:
shashank.ism wrote:A circle passes through the vertex C of rectangle ABCD and touches its sides AB and AD at P and Q respectively. If the distance from C to the line segment PQ is equal to 4 units, then the area of the rectangle ABCD in sq. units (is)

20
12
16
greater than 20
none of these
Hmmm, by "touches" do you mean "intersect with once" or "is tangent to"? I've never seen that wording before...

The golden rule:-"touches" always means it is a tangent.

Anyways shashank,thanks for the figure.
Now,tangent is always perpendicular to the radius. PQ = radius x sqrt(2).
Suppose C intersects PQ in F.By symmetry,CF passes through the centre
CF=4 units.
CF = radius + x
area = 4r^2

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ldoolitt: Master | Next Rank: 500 Posts; Posts: 184; Joined: Sat Apr 14, 2007 9:23 am; Location: Madison, WI; Thanked: 17 times

by ldoolitt » Tue Feb 09, 2010 1:37 pm

harsh.champ wrote:
ldoolitt wrote:
shashank.ism wrote:A circle passes through the vertex C of rectangle ABCD and touches its sides AB and AD at P and Q respectively. If the distance from C to the line segment PQ is equal to 4 units, then the area of the rectangle ABCD in sq. units (is)

20
12
16
greater than 20
none of these
Hmmm, by "touches" do you mean "intersect with once" or "is tangent to"? I've never seen that wording before...
The golden rule:-"touches" always means it is a tangent.

Anyways shashank,thanks for the figure.
Now,tangent is always perpendicular to the radius. PQ = radius x sqrt(2).
Suppose C intersects PQ in F.By symmetry,CF passes through the centre
CF=4 units.
CF = radius + x
area = 4r^2

Hmm, I guess I've never heard that term before. Oh well.

Thats a good solution.

Luke

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