Question

Two parallel chords of lengths 30 cm and 16 cm are drawn on the opposite sides of radius 17 cm. Find the distance between the chords.​

Answer 1

Answer:

Step-by-step explanation:

Let the center of the of the circle is O and radius is 17 cm.

Two parallel chords of length 30 cm and 16 cm are drawn on the opposite side of the center.

Draw altitudes on the cords from the center O. The altitudes divide each of the chord in two equal parts.

Answer 2

Solution :

Let AB and CD be two chords of a circle such that AB is parallel to CD and they are on the opposite sides of the centre.

Given:

$\implies$ AB = 30 cm

$\implies$ CD = 16 cm

Construction:

Draw OL ⊥ AB and OM ⊥ CD. Join OA and OC. Now, we know that, OA = OC = 17 cm (Radii of a circle). The perpendicular from the centre of a circle to a chord bisects the chord.

Therefore:

$\implies$ AL = (AB/2)

$\implies$ AL = (30/2)

$\implies$ AL = 15 cm

Now, in right angled ΔOLA, we have:

$\implies$ OA² = AL² + LO²

$\implies$ LO² = OA² - AL²

$\implies$ LO² = 17² - 15²

$\implies$ LO² = 289 - 225

$\implies$ LO² = 64

$\implies$ LO = 8 cm

Similarly,

In right angled ΔCMO, we have:

$\implies$ OC² = CM² + MO²

$\implies$ MO² = OC² - CM²

$\implies$ MO² = 17² - 8²

$\implies$ MO² = 289 - 64

$\implies$ MO² = 225

$\implies$ MO = 15 cm

Hence,

Distance between the chords:

$\implies$ (LO + MO)

$\implies$ (8 + 15) cm

$\implies$ 23 cm

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Answered by: Niki Swar, Goa❤️