Question

What will be the diameter of the crircle with paraliel chords of length 6 cm and 8 cm inone side of the centre and the distance between two chords is one centimeter-​

Answer 1

Answer:

diameter = 10 cm

Step-by-step explanation:

The half of the chord lengths being 3 cm and 4 cm respectively.

x² + 4² = r²    ----- (1)

Distance between two chords is 1 cm.

Let the distance of the longer chord be 'x' cm.

(x+1)² + 3² = r²     ------- (2)

On solving both, we get

=> x² + 4² = (x + 1)² + 3²

=> x² + 16 = x² + 1 + 2x + 9

=> 2x = 6

=> x = 3

Place x = 3 in (1),

3² + 4² = r²

=> 9 + 16 = r²

=> r = 5 cm

Then,

diameter = 2r = 10 cm

Therefore, diameter is 10 cm.

Hope it helps!

Answer 2

Let AB and CD are two parallel chords of a circle having length 6 cm and 8 cm and radius is O.

Let the radius of the circle be r.

Now draw OP perpendicular to AB and OQ perpendicular to CD.

since OP is perpendicular to AB and OQ is perpendicular to CD and AB || CD

From figure, OP = 4 cm.

P, Q are the mid points of AB and CD respectively. [perpendicular from center bisects the chord]

So AP=PB= AB/2=6/2=3cm

CQ=QD=CD/2=8/2= 4 cm

Now in triangle OAP

$oa^{2} = op {}^{2} + ap {}^{2} \\ r {}^{2} { = 16 + 9 } \\ r = \sqrt{16 + 9 } \\ r = 5$

diameter = 2*5

=10 cm