Question 73

In a cirele with radius 5 cm, a chord is at a distance of 3 cm from the centre. The length of the chord is:

Solution

$$\triangle$$ OPB is right angle triangle.

($$\because$$ radius cuts the chord at right angle and equal parts.)

From the Pythagoras theorem,

$$(OB)^2 = (OP)^2 + (PB)^2$$

$$5^2 = 3^2 + (PB)^2$$

$$(PB)^2 = 25 - 9 = 16$$

PB = 4

AB = 2PB = 2 $$\times$$ 4 = 8 cm

$$\therefore$$ The length of the chord is 8 cm.

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