Geometry

Tangent and Secant Lines

Circles - Intersecting Chords

         

Let rr be the radius of the above circle centered at O.O. If PD=10,PC=15\begin{array}{c}\displaystyle \lvert{\overline{PD}}\rvert=10, & \lvert{\overline{PC}}\rvert=15\end{array} and PP is the midpoint of OB,\overline{OB}, what is r2?r^2?

The lengths of some line segments in the figure above are AP=9,BP=6,OD=9.\begin{array}{c}\displaystyle \lvert{\overline{AP}}\rvert=9, & \lvert{\overline{BP}}\rvert=6, & \lvert{\overline{OD}}\rvert=9.\end{array} If OP=x,\lvert{\overline{OP}}\rvert=x, then what is the value of x2?x^2 ?

The lengths of some line segments in the figure above are AP=13,CP=17,DP=8.\begin{array}{c}\displaystyle \lvert{\overline{AP}}\rvert=13, & \lvert{\overline{CP}}\rvert=17, & \lvert{\overline{DP}}\rvert=8.\end{array} Then what is BP?\lvert{\overline{BP}}\rvert ?

If the lengths of some line segments in the figure above are AP=6,OB=8,CP=x,\begin{array}{c}\displaystyle \lvert{\overline{AP}}\rvert=6, & \lvert{\overline{OB}}\rvert=8, & \lvert{\overline{CP}}\rvert=x,\end{array} then what is the value of x2?x^2 ?

In the above circle centered at O,O, let OD=16,\lvert{\overline{OD}}\rvert=16, CD=8\lvert{\overline{CD}}\rvert=8 and ODAB.\overline{OD} \perp \overline{AB}. Then what is the value of CA2?\lvert{\overline{CA}}\rvert^2 ?

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