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2 years ago

In the diagram, the radius is 7 and tangent AB has length of 24. Determine the length of OA rounded to the nearest whole number

Mathematics

1 answer:

katen-ka-za [31]2 years ago

7 0

Given the radius r and the tangent line AB, the length of the line OA is 24 units

<h3>How to determine the length OA?</h3>

The radius r and the tangent line AB meet at a right angle.

By Pythagoras theorem, we have:

AB² = OA² + r²

So, we have:

24² = OA² + 7²

Rewrite as:

OA² = 24² - 7²

Evaluate

OA² = 527

Take the square root of both sides

OA = 23

Hence, the length of OA is 24 units

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bixtya [17]

Answer:

$AB=2\sqrt{ab}$

Step-by-step explanation:

From figure,

$OA=a, \quad \quad O'B=b\\\Rightarrow OO'= (a+b) \quad \quad \text{and}\quad OD=(a-b)$

In triangle $OO'D$

$(OO')^2=(OD)^2+(O' D)^2$

$\Rightarrow (a+b)^2=(a-b)^2+(O' D)^2\\\Rightarrow a^2+b^2+2ab-a^2-b^2+2ab=(O' D)^2\\\Rightarrow 4ab=(O' D)^2\\\Rightarrow O'D=2\sqrt{ab} \\\Rightarrow O' D=2\sqrt{ab}=AB \quad \quad [\because O' DAB\;\; \text{is a rectangle.}]$

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3 years ago

The area of a compact disc is 78.53 square centimeters. What is the radius of the disc? Use pi = 3.14

Tom [10]

Answer:

r = 5 cm

Step-by-step explanation:

A = πr²

78.53 = (3.14)r²

divide by 3.14

25 = r²

r = ±5

r = 5

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3 years ago

A snail can crawl 2/5 of a meter in a minute.

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Hope this helps!

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