PLEASEEEEEEE HELP ME!

Mathematics

1 answer:

posledela2 years ago

8 0

Answer:

DC = 6

Step-by-step explanation:

Given in the question,

radius = 3x

tangents to the circle = 12 + 5x and 8 + 7x

If you draw line from A to D, two right angle triangle will be form ADC and ADB

having radius = 3x

<h3>By using pythagorus theorem</h3><h3>hypotenuse² = base² + height²</h3><h3 />

Since, both triangle share same hypotenuse AD

so,

<h3> ΔADC ΔADB</h3><h3>base² + height² = base² + height²</h3><h3 />

3x² + (8 + 7x)² = 3x² + (12 + 5x)²

3x² will be cancel out

(8 + 7x)² = (12 + 5x)²

64 + 112x + 49x² = 144 + 120x + 25x²

rearranging like terms

49x²-25x² +112x - 120x + 64 -144 = 0

24x² - 8x - 80 = 0

(x- 2)(x + 5/3)

x = 2

x = -5/3 rejected as radius can't be negative

So,

length of radius = 3x = 6

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Hope this helps!!

If I am wrong, please tell me, I enjoy learning from my mistakes:)

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