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Circle

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)

20
12
16
greater than 20
none of these
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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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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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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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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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