Question

Using the circle below, solve for the length of ST. The diameter of the circle is 20 and TR=6

Answer 1

Step-by-step explanation:

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Answer 2

Given:

From the given figure,

The length of the line TR = 6 cm.

The diameter of the circle = 20 cm.

To Find:

We have to solve for the length of the line ST using the given figure.

Solution:

Given, the diameter of the circle = 20 cm.

∴, Radius of the circle = $\frac{Diameter}{2}$

Radius, SR = $\frac{20}{2} = 10 cm.$

Since, Δ STR is a right triangle, we can use Pythagoras Theorem.

Pythagoras Theorem is given by:

$(Hypotenuse)^{2} = (Base)^{2} + (Altitude)^{2} .$

Here, ST is the altitude of the triangle.

Substituting the values in the above equation, we get,

$(10)^{2} = (6)^{2} + (ST)^{2}$

$100 = 36 + (ST)^{2}$

$i.e., (ST)^{2} = 100 - 36 = 64$

∴, $ST = \sqrt{64} = 8 cm.$

Hence, the length of the line ST is 8 cm.

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