Question

O is centre of circle. PT and PQ are tangents to circle from point P. angle TPQ = 70 degree. find angle TRQ

Answer 1

take OT and OQ as radii on a circle..extend them outside to a point P outside the circle..and extend two extra lines again to a point  R..u get a diagram..now join O(center) and P..OP..prove OTP and OQP by congruency(OTP=OQP{as 90 degrees},OP=OP(common line),OT=OQ(radii))..and hence result comes this proof angle OTP = angle  OQP =90 degrees..as given angle TPQ=70 degrees,so in quad PTOQ, 90+70+90+QOT=360,QOT =110. we know an angle subtended by an arc at the centre is double the angle subtended by the same arc at any point on the circle..consider arc QT subtends angle QOT at the centre and QRT at point R..so QOT= 2 * QRT, QRT = 110/2, QRT=55 degrees(answer) Happy To Help :)