Geometry
# Tangent and Secant Lines

\(\overline{PT}\) is tangent to both circle \(O\) and circle \(O'\) at the same point \(T,\) while \(\overline{PAB}\) and \(\overline{PCD}\) are secant lines to circle \(O\) and circle \(O',\) respectively. Given the following three lengths: \[\lvert{\overline{AB}}\rvert=25, \lvert{\overline{PC}}\rvert=6, \lvert{\overline{CD}}\rvert=8,\] what is \(\lvert\overline{PA}\rvert?\)

**Note:** The above diagram is not drawn to scale.

\(\overline{PT}\) is tangent to circle \(O\) at point \(T,\) while \(\overline{PAB}\) is a secant line to the circle. If \[\lvert\overline{PA}\rvert=16 \text{ and } \lvert\overline{AB}\rvert=6,\] where \(\lvert\overline{PA}\rvert\) denotes the length of \(\overline{PA},\) what is \(\lvert\overline{PT}\rvert ?\)

**Note:** The above diagram is not drawn to scale.

\(\overline{PT}\) is tangent to circle \(O\) at point \(T,\) and we are given the following two lengths: \[\lvert{\overline{PT}}\rvert=22 \text{ and } \lvert{\overline{PA}}\rvert=18.\] What is the radius of circle \(O ?\)

**Note:** The above diagram is not drawn to scale.

In the above figure, \(A, B\) and \(T\) are three points lying on a circle. If \(\overline{PT}\) is a tangent line of the circle and \[\lvert\overline{AB}\rvert=7 \text{ and }\lvert\overline{PT}\rvert=12,\] where \(\lvert\overline{AB}\rvert\) denotes the length of \(\overline{AB},\) what is \(\lvert\overline{PA}\rvert ?\)

**Note:** The above diagram is not drawn to scale.

×

Problem Loading...

Note Loading...

Set Loading...