Question

PQ and RS are the two parallel chords of a circle whose center is O and radius is 10cm. If PQ = 16m and RS=12cm find the distance between PQ and RS when they lie on the same side of center O and on the opposite side of center O

Answer 1

Answer:

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Answer 2

Given that,

PQ and RS are the two parallel chords of a circle whose center is O

Radius = 10 cm

Length of first chord = 16 m

Length of Second chord = 12 m

According to figure,

We need to calculate the distance OM

Using pythagorean theorem

$OM^2=OP^2-PM^2$

Put the value into the formula

$OM=\sqrt{10^2-8^2}$

$OM= 6\ m$

We need to calculate the distance ON

Using pythagorean theorem

$ON^2=OR^2-RN^2$

Put the value into the formula

$ON=\sqrt{10^2-6^2}$

$ON= 8\ m$

(a). When both parallel chords PQ and RS in opposite side of center

We need to calculate the distance between two parallel chords PQ and RS

Using formula for distance between PQ and RS

$MN=ON+OM$

Put the value into the formula

$MN=8+6$

$MN=14\ m$

(b). When both parallel chords PQ and RS in same side of center

We need to calculate the distance between two parallel chords PQ and RS

Using formula for distance between PQ and RS

$MN=ON-OM$

Put the value into the formula

$MN=8-6$

$MN=2\ m$

Hence, (a). The distance between two parallel chords PQ and RS is 14 m.

(b). The distance between two parallel chords PQ and RS is 2 m.