Geometry

Tangent and Secant Lines

Tangent-Secant

         

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

Note: The above diagram is not drawn to scale.

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

Note: The above diagram is not drawn to scale.

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

Note: The above diagram is not drawn to scale.

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

Note: The above diagram is not drawn to scale.

From a point PP outside of the circle, 2 lines are drawn which intersect the circle at AA and BB, CC and DD respectively. If PA=16 |PA| = 16 , PB=7|PB| = 7 and PC=4 |PC| = 4 , what is the length PD |PD| ?

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