Question

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Answer 1

$\huge{\mathtt{\underline{\underline{QUESTION}}}}$

Radius of circle is 10 cm. There are two chords of length 16 cm each. What will be the distance of these chords form the centre of the circle?

$\huge{\mathtt{\underline{\underline{ANSWER}}}}$

Let two chords be AB and CD

AB = CD = 16cm

Radius = AO = 10cm

Let OE be the prependicular drawn from the centre of the circle to chord AB .

Prependicular drawn from the centre of the circle to a chord bisects the chord .

So, AE = EO = 8cm

In ∆ AEO,

(EO)² + (AE)² = (AO)²

(EO)² + (8)² = (10)²

(EO)² + 64 = 100

(EO)² = 100 - 64

(EO)² = 36

(EO)² = $\sqrt{36}$

${\boxed{\bold{EO\:=\:6cm}}}$

Now, we know that congruent chords of a circle are equidistant from the centre .

∴ EO = OF = 6cm

Distance of these chord from the centre is,

=> EO + OF

=> 6cm + 6cm

$\huge{\boxed{\mathtt{\red{12cm}}}}$

Answer 2

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