Properties of the Circle

 

Solid Geometry

Solid Geometry (also known as Solid Mensuration) is the study of various solids. It is the study of the measure of volume, area, height, length, and many more. This subject is used extensively in the practice of engineering. The knowledge of this subject is a necessity to engineers in any project construction.

This subject will cover the following: Cube, Rectangular Parallelepiped, Prism, Cylinder, Cone, Frustums, Spheres, Solids of Revolution, Prismatoid, etcetera.

Circles having different radii are similar.

The central angle which intercept an arc double of any inscribed angle that intercepts the same arc.

The radius perpendicular to a chord bisects the chord.

The chords equidistant from the center are equal in length. 

Angles in Same Segment of Circle are Equal

Let ABCD be a circle, and let ∠BAD,∠BED be angles in the same segment BAED.

Let F be the center of ABCD, and join BF and FD.
From the Inscribed Angle Theorem:

• ∠BFD=2∠BAD
• ∠BFD=2∠BED

So ∠BAD=∠BED.
Hence the result.

Segments of a Circle

A chord of a circle divides the circle into two regions, which are called the segments of the circle. The minor segment is the region bounded by the chord and the minor arc intercepted by the chord. The major segment is the region bounded by the chord and the major arc intercepted by the chord. Angles in Different Segments Angles in the Same Segment Read Videos Tangent   The limaçon trisectrix: a curve with two tangents at the origin Two pairs of tangent circles. Above internally and below externally tangent