# Gemotry of circle and right angle

• quantum_enhan
In summary, the conversation discusses finding the value of x using trigonometry and Pythagorean theorem. The 90 degree angle in the diagram is directed along the middle of the circle, and drawing a line from the circle's point of contact to the center of the circle would create a 45 degree angle with the vertical. The calculations for finding x are then discussed, with the conclusion that the last angle in the quadrilateral is also 90 degrees. The conversation also mentions an alternative method for solving the problem using only Pythagorean theorem.
quantum_enhan

ALright, just a quick question concerning this diagram. Since the 90 degree angle is directed along the middle ove the circle, does that mean if you draw a line from where the circle is touching the ninety degree angle to the centre of the circle, it would make a 45 degree angle with the vertical of the centre of the circle and the nine degree angle?

For example, to find x, would I go:

cos 45deg = 2inch/b
b=2.83
thus x = 2.83-0.5 = 2.33

From the centre to one of the contacts it's 90o, from the centre to the other point of contact it's 90o and the 3rd angle given is 90o, by the sum of quadrilaterals property the last angle is...?

90 degrees. So then the calculations would be correct, would they not? Since the center of the circle is below the metal block, we would just add 0.5 to to answer calculated from the triangle? ps thank u

Sorry about the late reply. Yes, that's correct. You could also solve it without using any trigonometry as follows:

The height from the ground to the top of the triangle is x+2.5
The height from the centre of the circle to the top of the triangle is - by pythagoras' theorem - $$2\sqrt{2}$$ thus for the total height it is $$2+2\sqrt{2}$$.

Therefore $$2+2\sqrt{2}=x+2.5$$

But really it just switches from using trigonometry to using pythagoras' theorem so it's essentially the same.

## 1. What is a circle?

A circle is a shape that is defined as a set of all points in a plane that are equidistant from a given point, known as the center.

## 2. What is the formula for finding the circumference of a circle?

The formula for finding the circumference of a circle is C = 2πr, where C is the circumference and r is the radius of the circle.

## 3. How do you find the area of a circle?

The formula for finding the area of a circle is A = πr^2, where A is the area and r is the radius of the circle.

## 4. What is a right angle?

A right angle is an angle that measures exactly 90 degrees. It is formed when two lines intersect and create four 90-degree angles.

## 5. How do you determine if two lines are perpendicular?

Two lines are perpendicular if they intersect at a right angle, meaning the angle between them is exactly 90 degrees.

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