S is the circumcircle of △ABC. Bisectors of ∠A, ∠B, ∠C meet S at P, Q, R respectively. I is the incenter of △ABC.
1: Prove that I is orthocenter of △P QR.
2: Given m∠P = 70, m∠Q = 54, find m∠A.
3: Given BI = 6, BR = 8, BP = 10, find P R.
4: Given m∠P IR = 110, find m∠ABC.

Find the value of the cosine for angle a

Successful implementation of a new system is based on three independent modules. module 1 works properly with probability 0.96. for modules 2 and 3, these probabilities equal 0.95 and 0.90. compute the probability that at least one of these three modules fails to work properly.

Acylinder and its dimensions are shown. which equation can be used to find v, the volume of the cylinder in cubic centimeters?