Final answer:
In Geometry, tangents from the same external point to a circle are congruent, meaning they are of equal length. This mathematical concept is predicated on geometric properties that ensure the equality of tangents based on congruent triangles formed by tangents and radii.
Step-by-step explanation:
Properties of Tangents from an External Point
The statement regarding tangents drawn from an external point to a circle refers to a fundamental concept in Mathematics, specifically in the area of geometry. This concept is based on the geometric property that tangents drawn from the same external point to a circle are congruent, which means they are equal in length. This property is often used in various geometric proofs and in solving problems related to circles and tangents.
The principle that both tensions would be equal if the angles on either side of the tangents are the same, relates to principles of physics but also applies to the geometric property that the angles formed by the tangent and the line joining the points of tangency to the external point (the radii) are equal. This geometric property allows for the creation of congruent triangles when a tangent is drawn from an external point, further confirming the equality of the tangents.
Moreover, the slope of the tangent at the point of contact is equal to the slope of the radius drawn to the tangent point, forming a right angle with it. This right angle and the equal radii contribute to the congruence of the triangles mentioned previously.