Answer:
To solve for x in a circle, you need to use some geometry concepts such as Pythagoras’ theorem, inscribed angles, and tangents. I’ll try to explain how to solve each problem.
For the left problem, you can use the fact that the diameter of the circle is 4, which means the radius is 2. Then you can use Pythagoras’ theorem to find the length of x. The theorem states that for a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. In this case, the hypotenuse is x and the other two sides are 2 and 4. So you can write:
x^2 = 2^2 + 4^2 x^2 = 4 + 16 x^2 = 20 x = √20 x ≈ 4.47
So x is approximately 4.47 units long.
For the right problem, you can use the fact that the triangle is a 3-4-5 right triangle, which means it has a 90° angle opposite to the side of length 5. Then you can use the inscribed angle theorem, which states that an angle inscribed in a circle is half of the central angle that subtends the same arc. In this case, the inscribed angle is 90° and the central angle is 180°, which means they subtend a semicircle. So the diameter of the circle is equal to the side of length 5. Therefore, x is 5 units long.
Explanation: