10.1 Angles in a circle

Circles are among the most important shapes in Geometry. It is simply an enclosed curve that has various parts. We can compute for its circumference and its area using some formula for circles or we can use the different parts to solve for the circle’s dimension.

In this chapter we will discuss about these parts. In 10.1 we will be discussing the angles found in a circle. First, there’s the Central angle, which is named as such because its vertex is the center of the circle and the sides are both radii of the circle. The intercepted arc that corresponds to the central angle is called the minor arc and has the same measurement as the central angle. The remaining section of the circle is called the major arc which has a measure of 360 degrees minus the measurement of the minor arc. Second, there’s the inscribed angle which has it vertex along the any point of the circle.

In 10.2 we will be looking at another part of the circle which is the chord. Chords are simply lines made from connecting two points on the circle. The diameter is an example of a chord. There are different chord properties that we will be learning like any two congruent chords would mean that there are also two congruent central angles, and two congruent arcs. We are also going to look at the perpendicular bisector. This is a line that bisects a chord and passes through the center of the circle.

We are also going to look into tangents for the last part of the chapter. Tangents are any line that touches one point on the circle. This point on the circle is referred to as the point of tangency. We are also going to look at some properties of the tangent like if a tangent of a circle intersects with a radius of the circle, they make two right angles.

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Angles in a circle

In a circle, chords, angles, inscribed angles and arc length all have special relationships with each other. This lesson focuses on exploring the relationships among inscribed angles in a circle as well as those of inscribed angle and central angle with the same arc. We will make use of the relationships to solve related questions in this lesson.


  • 1.
    In the following diagram, the radius is 24 cm and \angleBDC is 75°.

  • 3.
    Given \angleBAE = 44.5° and \angleADC = 64.27°.

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Angles in a circle

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