Question

the diameter of a circle is 20 CM there are two parallel chords of length 16 cm and 12 cm find the distance between these chord if chord are on the same side second opposite side of the centre​

Answer 1

Answer:

I) chords on the oppo: sides

d1=vr^2-(C/2)^2

=v10^2-8^2 = 6cm

d2=v10^2-6^2 = 8cm

d1 +d2=8+6=14cm. Ans

2) chords on the same side

d2-d1=8-6=2cm. .. Ans

Answer 2

The distance between two parallel chords when chords lie on same side =2 cm

The distance between two parallel chords when chords lie on opposite side of center=14 cm

Step-by-step explanation:

Diameter of circle=d=20 cm

Radius of circle =$\frac{d}{2}=\frac{20}{2}=10 cm$

Length of AF=16 cm

Length of BE=12 cm

We know that

Perpendicular drawn from center to the chord bisects the chord

Therefore, AP=PF=$\frac{1}{2}(16)=8 cm$

BD=DE=$\frac{1}{2}(12)=6 cm$

In triangle OPA

$OA^2=AP^2+OP^2$

Using Pythagoras theorem

$(Hypotenuse)^2=(Base)^2+(Perpendicular\;side)^2$

Substitute the values then we get

$(10)^2=(8)^2+OP^2$

$100=64 +OP^2$

$OP^2=100-64=36$

$OP=\sqrt{36}=6 cm$

In triangle OBD

$(OB)^2=OD^2+BD^2$

$(10)^2=OD^2+(6)^2$

$100=36+OD^2$

$100-36=OD^2$

$OD^2=64$

$OD=\sqrt{64}=8 cm$

OD-OP=8-6=2 cm

Hence, the distance between two parallel chords=2 cm

If chords lie on opposite side

Then, distance between two chords=8+6=14 cm

#Learns more:

https://brainly.in/question/3084316:Answered by Lalablackmama