Tangent to a Circle
📐 What is a Tangent?
A tangent to a circle is a straight line that touches the circle at exactly one point. This special point is called the point of tangency (or point of contact).
Think of a wheel resting on a flat road. The road touches the wheel at exactly one point — that's a tangent line!
🔑 Key Properties of a Tangent
Property 1: Perpendicularity
A tangent to a circle is always perpendicular (at 90°) to the radius drawn to the point of tangency.
If $OA$ is the radius and line $l$ is the tangent at point $A$, then:
$OA \perp l$
This means $\angle OAP = 90°$ where $P$ is any point on the tangent line.
Property 2: Equal Tangent Lengths
Two tangents drawn from the same external point to a circle are equal in length.
If $PA$ and $PB$ are tangents from external point $P$ to a circle with center $O$, then:
$PA = PB$
Also, $\angle OPA = \angle OPB$ (the line $OP$ bisects the angle between the tangents).