in a circle two parallel chords on the same side of a diameter have lengths 4cm and 6cm. If the distance between the chords is 1cm, then the diameter of the circle is
Answers
Answer:
Let the 6 cm long chord be x cm away from the centre of the circle. Let the radius of the circle be r cm.
The perpendiculars from the centre of the circle to the chords bisect the chords.
r
2
=
x
2
+
3
2
=
(
x
+
1
)
2
+
2
2
Solving,
x
=
2
and
r
=
√
13.
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Answer:
Let two | | cords AB=4 cm and PQ= 6 cm long are in a circle of center O and
radius r cm.. Draw perpendicular OD on AB and OR on PQ.
It is given RD= 1 cm. , RD=OD-OR. or. 1= OD-OR
OD= OR+1……………(1)
In right angled triangle ODA. , OD^2+AD^2=OA^2
or. (OR+1)^2+(4/2)^2= r^2
or. (OR+1)^2+4 = r^2…………………(2)
In right angled triangle ORP. , OR^2+PR^2= OP^2
or. OR^2+(6/2)^2= r^2
or. OR^2 + 9. = r^2……………..(3)
Subtracting eqn (3) from (2)
(OR+1)^2-(OR)^2–5=0
OR^2+2.OR+1 - OR^2 -5=0
2.OR=4. => OR =2. , putting OR=2 in eqn. (3)
2^2+9=r^2 => r=√13 cm.
Circumference of the circle=2.π.r =2.π.√13 = 2√13.π cm.
Step-by-step explanation:
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