I a triangle ABC if angle A =60 and the altitudes from Band C meet AC & AP at P and Q respectively and intersect each other at I prove that APIQ and PQBC and are cyclic quadrilaterals hence find the measure of angle BIC Share with your friends Share 5 Anuradha Sharma answered this In quadrilateral AQIP, ∠A=60 degree∠AQI=∠API=90 degreeSo ∠PIQ=360-90-90-60=120 degreeSo we can see that in quadrilateral AQIP ,∠A+∠PIQ=180 and ∠AQI+∠API=180SO APIQ is a cyclic quadrilateral.Now in triangle ABP, angle APC is a external angle So 90=60+∠1∠1=30 degreeand in triangle AQC, angle BQC is a external angle so 90=60+∠2∠2=30 degreeSO ∠1=∠2So we can see that it is only possible when PQBC are cyclic qudrilateral. 14 View Full Answer