Segment Products and Power of a Point: Practice

Chords have orders $A,P,B$ and $C,P,D$. The lengths $PA,PB$ are $x,x+2$, and $PC,PD$ are $3,8$. Here $x$ is a length. Find $x$.

A secant has external length $x$ and inside chord length $7$. A tangent from the same point has length $\sqrt{30}$. Here $x$ is a length. Find $x$.

Secants have orders $P,A,B$ and $P,C,D$. The lengths $PA,AB,PC$ are $6,10,8$. Find $CD$.

A tangent has length $\sqrt{55}$. A secant from the same external point has external length $5$. Find its inside chord length.

A circle has radius $12$ and an interior point at center distance $9$. Which pair gives signed power and positive chord-part product?

A circle has radius $12$. The signed power of external $P$ is $81$. Find $OP$.

A circle has radius $7$ and $OP$ is $1$. A chord through $P$ has $PA$ of $7$. Find $PB$.

A tangent segment has length $x+1$. A secant from the same external point has external length $2$ and whole length $18$. Find the valid parameter $x$.

An external secant has lengths $x+8$ to the near endpoint and $x+12$ to the far endpoint. A tangent from the same point has length $3\sqrt5$. Here $x$ is a parameter. Find every valid $x$.

For two distinct secants with orders $P,A,B$ and $P,C,D$, which ordered similarity matches triangle $PAD$?

A tangent at $T$ and a secant $P,A,B$ start at external $P$. Which ordered similarity matches triangle $PTA$?

Point $P$ coincides with endpoint $A$ on a circle, and a secant has the other endpoint $B$. Which factor makes $PA\cdot PB$ zero?