Segment Products and Power of a Point: Practice

Chords have orders $A,P,B$ and $C,P,D$ in one circle. Which product equality follows?

Chords $AB,CD$ meet at interior $P$. The lengths $PA,PB,PC$ are $6,7,3$. Find $PD$.

On a secant in order $P,A,B$, external length $PA$ is $5$ and inside chord $AB$ is $8$. Find the whole $PB$.

Two secants have orders $P,A,B$ and $P,C,D$. The lengths $PA,PB,PC$ are $3,16,4$. Find $PD$.

A tangent segment $PT$ and secant $P,A,B$ come from the same external point. The external and whole secant lengths are $4,9$. Find $PT$.

A circle has radius $7$ and $OP$ is $3$. Find the signed power of $P$.

A circle has radius $8$ and $OP$ is $10$. Find the signed power of $P$.

A point $P$ lies on a positive-radius circle. Which statement is correct?

An interior point has signed power $-18$. What is the positive product of the two parts of any chord through it?

A secant from external $P$ has external length $5$ and inside chord length $7$. What is the square of a tangent segment from $P$?

For general intersecting chords in orders $A,P,B$ and $C,P,D$, which ordered similarity matches triangle $APC$?

A strict external point has signed power $49$. Find a tangent segment length from that point.