the maximum number of tangent that can be drawn to a circle from a point outside it is....
Answers
Answer:
2
Step-by-step explanation:
To Find:- Maximum number of tangent that can be drawn to a circle from an outside point.
Solution:-
Tangent is derived from a Latin word 'tangere' which means "to touch".
In Geometry, tangent is defined as a line that touches a curved surface at exactly one point.
A tangent of a circle is a straight line that intersects or touches the circle at only one point. It never enters the circle’s interior. It touches the circle’s radius at the point of tangency at a right angle.
The two most important theorem's of a tangent of a circle are:
THEOREM 1: The tangent at any point on a circle is perpendicular to the radius at the point of contact.
THEOREM 2: When two tangents are drawn to a circle from an exterior point P. Let the points of contact be A and B, then
1. The lengths of the two tangents will be equal, i.e. PA = PB.
2. The two tangents will subtend equal angles at the center, that
is, ∠POA = ∠POB, where O is the center of the circle.
3. The angle between the tangents will be bisected by the line
joining the exterior point and the center which is PO, that is,
∠APO = ∠BPO.
From the figure we can observe than only two tangents can be drawn to a circle from an exterior point P i.e. PA and PB.
Hence, The maximum number of tangent that can be drawn to a circle from a point outside the circle is 2.
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