Tangent to a Circle
How to use the properties of the tangent to the circle: definition, 2 properties, 2 examples, and their solutions.
Definition
A tangent to a circle is a line
that touches the circle.
From a point exterior of the circle,
you can draw two tangents.
PropertyTangent and Radius
The tangent and the radius
are perpendicular
at the intersecting point of the circle.
Example
Ray PB is tangent to the given circle
at point B.
And OB is the radius.
So ray PB and OB are perpendicular.
OB is the radius.
OB = 5.
OA is also the radius.
So OA = 5.
See △OPB.
It's a right triangle.
The sides are (5, PB, 8 + 5) = (5, PB, 13).
So this right triangle is
a (5, 12, 13) right triangle.
Pythagorean Triple
So PB = 12.
So write 12.
So 12 is the answer.
PropertyTangent Segments
If two segments from an exterior point
are tangent to a circle,
then those two segments are congruent.
Example
The blue segments
start from the same point A.
They are tangent to the same circle.
So the blue segments are congruent:
7.
The green segments
start from the same point B.
They are tangent to the same circle.
So the green segments are congruent:
10.
The brown segments
start from the same point C.
They are tangent to the same circle.
So the brown segments are congruent:
5.
See △ABC.
There are 2 of 7, 10, and 5.
So the perimeter is
P = 2(7 + 10 + 5).
7 + 10 + 5 = 22
2⋅22 = 44
So 44 is the answer.