Question

the radius of a circle is 6cm . the perpendicular distance from the centre to the chord which is 8 cm in length is

Answer 1

we can solve it by Pythagoras theorem
we know that perpendicular to chord from center bisect the chord in two halves hence,
AB²+BC²=AC²
4²+x²=6²
16+x²=36
=2✓5

Answer 2

The answer is 2√5 cm

GIVEN

Radius of the circle = 6 cm

Chord of the circle = 8cm

TO FIND

The length of the perpendicular distance from the centre to the chord.

SOLUTION

We can simply solve the above problem as follows;

Let the diameter of the circle be 'O'.

Chord of the circle = AB = 8cm

Radius of the circle = OA = 6 cm

Let the perpendicular drawn from the centre of the circle = OC

Now,

We know that, The perpendicular from the centre of a circle to a chord bisects the chord.

Therefore,

AC = 4 cm

Applying Pythagoras theorem in ∆OAC

OC² = OA² - AC²

OC² = 6² - 4²

OC² = 36 - 16

OC² = 20

OC = √20 = 2✓5 cm

Hence, The answer is 2√5 cm

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