One tangent line, and only one, can be drawn to any point on the circumference of a circle, and this tangent is perpendicular to the radius through the point of contact. In the figure below, line is tangent to the circle at point .
If two tangents are drawn to a circle from an external point,
- the lengths of the tangents from the external point to the points of contact are equal;
- they subtend equal angles at the center of the circle.
In the figure below, and .
In the figure below, and are tangents to the circle at points and , respectively. If and , find .
Consider the diagram to the right.
- Opposite angles of a cyclic quadrilateral sum up to . So
- From the inscribed angle theorem, we can see that
Since the sum of interior angle of a quadrilateral is , we have
On the same side of a straight line three circles are drawn as follows:
- A circle with a radius of 4 cm is tangent to the line.
- The other two circles are identical, and each is tangent to the line and to the other two circles.
What are the possible radii of these two identical circles?
A. 24 cm only
B. 20 cm only
C.16 cm only
D. 24 and 20 cm only
E. 20 and 16 cm only
F. 16 and 24 cm only
G. 16, 20, 14 cm only
H. No solution
Note: A diagram has not been provided because drawing the correct diagram is part of the problem solving.