# Secant and Tangent Angles in Circles, finding an arc length.

• MHB
• Cj111
In summary, a secant angle in a circle is formed by a line that intersects the circle at two points, while a tangent angle is formed by a line that intersects the circle at one point. The measure of a tangent angle can be found using the formula measure = 1/2(180 - central angle). A secant angle and a tangent angle are complementary angles, with a sum of 90 degrees. The length of an arc in a circle can be found using the formula length = (central angle/360) x 2πr or the arc length formula, length = radius x central angle. Finally, the measure of a central angle can be found if the length of the arc and the radius of the circle are known
Cj111
View attachment 8161

I got 138.17, but that isn't correct. I don't know how to do it, since the only way I thought, gave me the wrong answer. Can anyone help?

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I would call point $C$ the center of the circle. So, what must the measures of $$\displaystyle \angle CPQ$$ and $$\displaystyle \angle CRQ$$ be?

To follow up, since $$\displaystyle \overline{QP}$$ and $$\displaystyle \overline{QR}$$ are tangent to the circle, we must have $$\displaystyle \angle CPQ=\angle CRQ=90^{\circ}$$. Since the sum of the interior angles of a quadrilateral is $360^{\circ}$, it follows then that:

$$\displaystyle 100x+81x-1=180\implies x=1$$

And hence, $$\displaystyle \overset{\frown}{PR}=100^{\circ}$$

## 1. What is the definition of a secant angle in a circle?

A secant angle is formed by a line that intersects a circle at two points, creating two arcs. The angle is formed by the two rays that extend from the center of the circle through the points of intersection.

## 2. How do you find the measure of a tangent angle in a circle?

A tangent angle is formed by a line that intersects a circle at one point, creating one arc. To find the measure of a tangent angle, use the formula measure = 1/2(180 - central angle).

## 3. What is the relationship between a secant angle and a tangent angle in a circle?

A secant angle and a tangent angle are complementary angles. This means that the sum of their measures is equal to 90 degrees. This relationship is true because a tangent line is perpendicular to a radius of a circle, creating a right angle with the secant line.

## 4. How do you find the length of an arc in a circle?

To find the length of an arc in a circle, you can use the formula length = (central angle/360) x 2πr, where r is the radius of the circle. You can also use the arc length formula, length = radius x central angle.

## 5. Can you find the measure of a central angle if you know the length of the arc?

Yes, you can use the formula central angle = (arc length/2πr) x 360, where r is the radius of the circle. You can also use the central angle formula, central angle = arc length/radius.

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