Circle r has a radius of 6, and qp is tangent to circle r at point q. also, qp = 8. (a) what is the measure of ∠rqp ? explain your answer. (b) what is the length of rp ? explain your answer. (c) what is the length of rs ? explain your answer. (d) what is the length of sp ? explain your answer.

RQ = 6; RS = 6 ; these are radius

The triangle formed is right triangle. ∠RQP = 90°

QP = 8 ; this is the long leg.
RQ = 6; this is the short leg
RP = ? is the hypotenuse

a² + b² = c²
8² + 6² = c²
64 + 36 = c²
100 = c²
10 = c

The hypotenuse is 10, but RS is part of the hypotenuse, it has a measure of 6.

6 + x = 10
x = 10 - 6
x = 4   length of SP