Question

A
(a) दी हुई आकृति में वृत्त की त्रिज्या 5 सेंटीमीटर है। जीवायें AB और
CD समान्तर हैं और उनके बीच की दूरी 7 सेंटीमीटर है। यदि
CD = 6 सेंटीमीटर है तो AB ज्ञात किजिए।
(पाठ 15 देखें)​

Answer 1

Given:

The radius of the circle is 5 cm

Chords AB  and CD are parallel and the distance between them is 7 cm

CD = 6 cm

To find:

AB

Solution:

We know,

A line passing through the centre of the circle and perpendicular to the chords of the circle must bisect the chord.

Since

OP ⊥ AB and PQ passes through the centre

∴ $\bold {AP = \frac{1}{2}AB }$ ....... (i)

and

OQ ⊥ CD and PQ passes through the centre

∴ $CQ = \frac{1}{2}CD$

$\implies CQ = \frac{1}{2} \times 6$

$\implies \bold{CQ = 3 \:cm}$ ....... (ii)

Considering Δ COQ and applying the Pythagoras theorem, we get

$OC^2 = OQ^2 + CQ^2$

substituting the value of OC = radius = 5 cm and the value of CQ from (ii)

$\implies 5^2 = OQ^2 + 3^2$

$\implies 25 = OQ^2 + 9$

$\implies OQ = \sqrt{25 - 9 }$

$\implies OQ = \sqrt{16 }$

$\implies \bold{OQ = 4\: cm}$

The distance between AB and CD i.e., PQ = OP + OQ = 7 cm (given)

∴ OP = PQ - OQ = 7 - 4 = 3 cm

Considering Δ AOP and applying the Pythagoras theorem, we get

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

substituting the value of OA = radius = 5 cm and OP = 3 cm

$\implies 5^2 = 3^2 + AP^2$

$\implies AP^2 = 25 - 9$

$\implies AP = \sqrt{25 - 9 }$

$\implies AP = \sqrt{16 }$

$\implies \bold{AP = 4\: cm}$ ...... (iii)

Substituting from (iii) in (i), we get

$AP = \frac{1}{2}AB$

$\implies 4 = \frac{1}{2} \times AB$

$\implies AB = 2 \times 4$

$\implies \bold{AB = 8\: cm}$

Thus, $\boxed{\bold{AB = \underline{8\: cm}}}$.

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Also View:

A circle is radius 5cm find the length of the chord of distance 3cm from its centre

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The length of two parallel chords of a circle are 6cm and 8cm. If the smaller chord is at a distance of 4cm from the centre, what is the distance of the other chord from the centre

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Answer 2

Answer:

(a) दी हुई आकृति में वृत्त की त्रिज्या 5 सेंटीमीटर है। जीवायें AB और CD समान्तर हैं और उनके बीच की दूरी 7 सेंटीमीटर है। यदि CD = 6 सेंटीमीटर है तो AB ज्ञात किजिए।

B

A

(पाठ 15 देखें)

In the given figure radius of the circle is 5 cm. Chords AB and CD are parallel and distance between them is 7 cm. If

CD = 6 cm, then find AB.