Question

A chord 6 cm long is drawn in a circle with a diameter equal to 10 cm. Find its perpendicular distance from the centre. (a) 4 cm (b) 7 cm (c) 6 cm (d) 5 cm

Answer 1

SOLUTION

TO CHOOSE THE CORRECT OPTION

A chord 6 cm long is drawn in a circle with a diameter equal to 10 cm. Find its perpendicular distance from the centre.

(a) 4 cm

(b) 7 cm

(c) 6 cm

(d) 5 cm

EVALUATION

Here it is given that A chord 6 cm long is drawn in a circle with a diameter equal to 10 cm

Let

AB = 6 cm

∴ CB = 3 cm

Diameter = 10 cm

∴ OB = 5cm

We have to find OC

In the context of the given problem, Pythagoras theorem states that '' For a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides ''

$\sf{ {(OB )}^{2} = {(OC )}^{2} +{(CB )}^{2} } \:$

$\implies \: \sf{ {(5 )}^{2} = {(OC )}^{2} +{(3 )}^{2} } \:$

$\implies \: \sf{ {(OC )}^{2} = {(5)}^{2} - {(3 )}^{2} } \:$

$\implies \: \sf{ {(OC )}^{2} = 25 - 9 } \:$

$\implies \: \sf{ {(OC )}^{2} = 16 } \:$

$\implies \: \sf{ OC = 4 } \:$

∴ OC = 4 cm

FINAL ANSWER

The correct option is (a) 4 cm

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Answer 2

Answer:

The answer is 4 cm

Step-by-step explanation:

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