Question

AB = 5, AP = 4, and DP = 12, then find the length of PC

Answer 1

`PC = 0.333`

Explanation:

Given

`AB = 5`

`AP = 4`

`DP =12\\`

See attachment

Required

Find PC

When two chords intersect, the product of the segments are always equal.

In chord DC, the segments are DP and PC

In chord AB, the segments are AP and PB

So:

`DP * PC = AP * PB`

This gives:

`12 * PC = 4 * PB` --- (1)

In chord AB, we have:

`AB = AP + PB`

Make PB the subject

`PB = AB - AP`

This becomes

`PB = 5 - 4`

`PB = 1`

`12 * PC = 4 * PB` --- (1) becomes

`12 * PC = 4 * 1`

`12 * PC = 4`

Make PC the subject

`PC = (4)/(12)`

`PC = 0.333`