Question

6.
What
will
be
the
diameter
of
the
circle
with
parallel
chords
of
length
6
cm
and
8
cm
in
one
side
of
the
centre
and
the
dis-
tance
between
two
chords
is
one
centime-
ter
B
6 cm
1 om
8 cm​

Answer 1

Answer:

Step-by-step explanation:

You can construct the center of the circle by:

drawing the perpendicular bisector of the longest chord (dashed blue line).

Connecting two nearby endpoints of the two chords (red line), and drawing its perpendicular bisector as well (red dashed line).

The intersection of these two bisectors is the midpoint of the circle M.

Together with the shortest chord these two bisectors form a (green) isosceles, with legs of length 4:

Now it is easy to see that that radius equals $\sqrt{(4)^{2}+(3)^{2}}$=5

Answer 2

Answer:

ans is 1cm

Step-by-step explanation:

Let AB=8 cm is the chord of the circle with radius 5 cm

Draw OP⊥AB and join BO

PB=

2

1

AB=

2

1

×8=4cm

In △BPO∠P=90

∘

∴OB

2

=PB

2

+OP

2

⇒OP

2

=OB

2

−PB

2

⇒OP=

5

2

−4

2

⇒OP=

25−16

⇒

9

=3cm.

Let CD=6 cm is the chord of the circle with radius 5 cm

Draw OQ⊥CD and join DO

QD=

2

1

CD=

2

1

×6=3cm

In △QDO∠Q=90

∘

∴OD

2

=QD

2

+OQ

2

⇒OQ

2

=OD

2

−QD

2

⇒OQ=

5

2

−3

2

⇒OQ=

25−9

⇒

16

=4cm.

PQ=OQ−OP=4−3=1cm

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