Question

If tangents PA and PB from a point P to a circle with centre O are inclined to each other at an angle of 100°, then ∟BOA is equal to ____________

pls answer fast

Answer 1

`m\angle BOA = 80\degree`

Explanation:

PA and PB are tangents to the circle with center O at points A and B respectively.

`\therefore OA \perp PA\:\: \& OB \perp PB....(\because tangent\perp radius)\\\therefore m\angle OAP=m\angle OBP = 90\degree\\m\angle APB = 100\degree\\OAPB \: is \: a\: quadrilateral\\\therefore m\angle APB+m\angle OAP+m\angle OBP+m\angle BOA = 360\degree\\\therefore 100\degree + 90\degree+ 90\degree+ m\angle BOA = 360\degree\\\therefore 280\degree + m\angle BOA = 360\degree\\\therefore m\angle BOA = 360\degree-280\degree \\\huge\red{\boxed{\therefore m\angle BOA = 80\degree}}`