Hello, students of Math Lobby! Today, we will be learning about the symmetrical properties of circles. These are very useful properties to understand as it will be helpful in application for solving certain types of questions related to circles. So, without further ado, let’s begin!
In this note, you will learn:
Symmetric Properties of Circles
· Perpendicular bisector of chord
· Equal chords
· Tangent perpendicular to radius
· Equal tangents
Symmetric Properties of Circles
1) Perpendicular bisector of chord
The perpendicular bisector of a chord of a circle passes through the center of the circle, i.e. XM = OM, OM ⊥ XY.
2) Equal chords
Chords that are equidistant from the center of a circle are equal in length,
i.e. WX = JK, OM = ON
3) Tangent perpendicular to radius
The tangent at the point of contact is perpendicular to the radius of a circle,
i.e. XY ⊥ OK
4) Equal tangents
Tangents from an external point are equal in length. The line from the center of a circle to an external point bisects the angle between the two tangents from the external point, i.e. XD = XE
And that’s all for today, students! Math Lobby hopes that after this article, you have a clear understanding on the symmetric properties of circles!
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