PA and PB are tangents to a circle with centre O if angle AOB = 120 degree then find - Maths - Areas Related to Circles

Question

PA and PB are tangents to a circle with centre O if angle AOB = 120
degree then find angle OPA

Anuradha Sharma · Accepted Answer

<img alt="" src=
"https://s3mn%20mnimgs%20com/img/shared/content_ck_images/images/DSSSSSS(1)%20png"
style="width: 343px; height: 214px;">
Since tangents and radius are perpendicular so∠OAP=∠OBP=90 degreeand by symmetry, ∠AOP=∠BOP=60 degreeSo in triangle OPA, ∠OAP+∠OPA+∠AOP=180∠OPA=180-90-60=30 degree

PA and PB are tangents to a circle with centre O. if angle AOB = 120 degree then find angle OPA.