Question

distance of a chord AB of a circle from the centre is 12cm and length of the chord AB is 10cm. find the diameter of the circle

Answer 1

Please see the attachment

Answer 2

The diameter of circle is 26 cm.

Given:

• Distance of a chord AB of a circle from the centre is 12cm.
• Length of the chord AB is 10cm.

To find:

• Find the diameter of the circle.

Solution:

Theorem to be used:

• Perpendicular from centre on chord bisects it.
• Pythagoras theorem can apply on right triangle. Hypotenuse²= Base²+ Perpendicular²

Step 1:

Draw the figure as shown in attachment.

It is clear that distance always measure perpendicular.

So,

OC is perpendicular on AB, where O is centre of circle.

Thus,

∆OCA is right triangle, right angle at C.

Step 2:

Apply Pythagoras theorem on ∆OCA.

∆OCA is right triangle.

Here

OC= 12 cm

CA= 5 cm

OA=?

AO²=OC²+CA²

$AO^2 = 144 + 25$

or

$AO^2= 169$

or

$\bf AO = 13$

Thus,

Radius of circle is 13 cm.

Step 3:

Find diameter of circle.

We know that

Diameter = 2× radius

So,

$Diameter = 2 \times 13$

or

$Diameter = 26 \: cm$

Thus,

Diameter of circle is 26 cm.

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