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in the arbor shown, AC and BC are tangents to circle D. The radius of the circle is 26 in and EC= 20 inches. find AC and BC to the nearest hundredth.​

in the arbor shown AC and BC are tangents to circle D The radius of the circle is 26 in and EC 20 inches find AC and BC to the nearest hundredth class=

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Kazeemsodikisola

Answer:

Step-by-step explanation:

Check attachment for solution and better understanding

AC and BC are tangent, then AC and BC will form a right angle with the radius of the circle

Given that,

EC = 20in

And Radius = 26in

Find AC and BC.

Though AC and BC are similar.

Taking Triangle ADC, check attachment, it is a right angle triangle.

Since it is a right angle triangle, we can apply Pythagoras theorem

DC² = AD² + AC²

46² = 26² + AC²

46² - 26² = AC²

AC² = 1440

AC = √1440

AC = 37.95 in

Also, taking triangle DBC

DC² = DB² + BC²

BC² = DC² - DB²

BC² = 46² - 26²

BC² = 1440

BC = √1440

BC = 37.95 in

Ver imagen Kazeemsodikisola
Ver imagen Kazeemsodikisola
boffeemadrid

The length of AC and BC is required.

The length of AC is 37.95 inch and BC is 37.95 inch.

Circles

DB = DE = 26 in (radius of the circle)

EC = 20 in

[tex]DC=DE+EC=26+20=46\ \text{in}[/tex]

BC is a tangent to the circle

So, [tex]\angle DBC=90^{\circ}[/tex]

Applying the Pythagoras theorem

[tex]DB^2+BC^2=DC^2\\\Rightarrow BC=\sqrt{DC^2-DB^2}\\\Rightarrow BC=\sqrt{46^2-26^2}\\\Rightarrow BC=37.95\ \text{in}[/tex]

Now, DB = DE = AD = 26 in (radius of the circle)

DC = 46 in

[tex]\angle DAC=90^{\circ}[/tex]

Similarly, AC will be equal BC equal to 37.95 in

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