Question

What is the length of RS?

Answer 1

Applying the Pythagoras Theorem, the length of RS = 8 units.

According to the figure,

Diameter = 16 +4 = 20 units

So, the Radius = Diameter/2 = 20/2 = 10 units

Now,

Let the center be M, then

MT = 10 - 4 = 6 units

RT = x units

The radius is perpendicular to the chord,

So, MTR will be a right-angled triangle,

We will apply the Pythagoras theorem,

So, we have :

$RT^{2} +TM^{2} =RM^{2}$

Here, RT = x units

TM = 6 units and RM = radius = 10 units

Putting these values in the Pythagoras theorem,

$x^{2} +6^{2} =10^{2}\\x^{2} + 36 = 100 \\x^{2} = 100 - 36 = 64\\x^{2} = 64 \\x = 8$

Thus, the length of RS = 8 units.

To read more about Pythagoras's theorem, visit brainly.com/question/343682

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