Question

AD is diameter of a circle and AB is a chord. If AB = 30cm and its perpendicular distance from the centre of the circle is 8 cm then what is the length of diameter AD

Answer 1

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Answer 2

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Answer:

34 cm

Step-by-step explanation:

Given:

- AB is 30 cm.

- Perpendicular distance from centre of circle = 8 cm

To determine: Length of Diameter AD

Since it is a perpendicular from the centre, as per the theorem, we know that it bisects.

Therefore, we can say AB/2 = 30/2 = 15 cm

Focusing on the bisected part of the chord as a base and the radius as hypotenuse, we notice that it forms a small right-angled triangle.

In previous grades, we have learned the Pythagoras theorem. In this question, we can apply the same:

$base^{2} + height^{2} = hypotenuse^2$

Substituting values:

$15^2 + 8^2 = radius^2$

$225 + 64= r^2$

$r^2 = 289r = \sqrt{289}$

  =  17 cm

We know that diameter is twice the value of radius, so:

r x 2 = d

17 x 2 = 34 cm = d

Hence, the length of diameter AD is 34 cm.

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