Skyhawk 172/Cutlass 172
Flight Crew Commercial; Flight Crew Instrument; Flight Crew Multiengine
Flight Crew Last 90 Days 15; Flight Crew Total 215; Flight Crew Type 175
Communication Breakdown; Situational Awareness
Conflict Airborne Conflict
Flight Crew Took Evasive Action
Human Factors; Weather
In a Cessna 172; we were in the traffic pattern for the LEFT runway and advised of traffic joining right traffic for a 2 mi final for the same runway; landing before us. I replied; 'Negative Contact.' The other Cessna was advised of landing helicopter traffic on the RIGHT runway. The other Cessna replied '(call sign); traffic in sight; no factor.' Tower cleared us to land and we began our turn to base believing that tower had cleared us to land without reporting 'traffic in sight' because the Cessna traffic was no factor. While on a turn to approximately a mile final we caught sight of the Cessna traffic turning from a right base to final that lined them up approximately in the middle of the two parallel runways. Since tower was operating under two different frequencies (one per active runway); we thought the Cessna was making traffic for the RIGHT runway and had possibly OVERshot their turn to final; so we UNDERshot our turn to final to give further separation. The other Cessna continued left into our final approach path less than 1/4 mile ahead and within 200 feet of our altitude. We initiated a go-around climb offsetting to the right and the other Cessna continued left of the final approach path in a dive. I believe that tower mistook the other aircraft's call for 'traffic in sight; no factor' as a call from us and thence cleared us to land. Since the other traffic was near and below we did not have a chance to see them on until we turned final. Both aircraft took evasive action once the conflict was realized. Significant winds may have played a role; as our aircraft's ground speed on base was much higher than the other traffic's.
C172 pilot reported a near NMAC encounter with another small aircraft in the traffic pattern at PRC.