Step-by-step explanation:
Theorem:
If two tangents are drawn to a circle from an external point to the circle, then the tangent segments are congruent.
Because of the theorem above, these pairs of segments are congruent:
PA, PB
RA, RC
SC, SB
Now look at PA and PB.
PA = PR + RA
PB = SP + SB
Since from above, RA = RC and SB = SC, substitute RA with RC and SB with SB in the two equations above. You get:
PA = PR + RC
PB = SP + SC
Now add the two equations above.
PA + PB = PR + RC + SC + PS,
but RC + SC = RS, so you get
PA + PB = PR + RS + SP
Switch sides to get
PR + RS + SP = PA + PB
