Answer:
[tex]PC = 0.333[/tex]
Step-by-step explanation:
Given
[tex]AB = 5[/tex]
[tex]AP = 4[/tex]
[tex]DP =12\\[/tex]
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:
[tex]DP * PC = AP * PB[/tex]
This gives:
[tex]12 * PC = 4 * PB[/tex] --- (1)
In chord AB, we have:
[tex]AB = AP + PB[/tex]
Make PB the subject
[tex]PB = AB - AP[/tex]
This becomes
[tex]PB = 5 - 4[/tex]
[tex]PB = 1[/tex]
[tex]12 * PC = 4 * PB[/tex] --- (1) becomes
[tex]12 * PC = 4 * 1[/tex]
[tex]12 * PC = 4[/tex]
Make PC the subject
[tex]PC = \frac{4}{12}[/tex]
[tex]PC = 0.333[/tex]
