 Hello and welcome to the session. I am Deepika here. Let's discuss a question which says choose the correct option and give justification. If tangents PA and PB from a point P to a circle with central O are inclined to each other at angle of 80 degree then angle POA is equal to A50 degree, B60 degree, C70 degree and D80 degree. Let us first understand the tangent to a circle. A tangent to a circle align that intersects the circle at only one point. So this is the key idea behind our question. We will take the help of this key idea to solve our question. So let's start the solution. Given tangents PA and PB from a point P to a circle with central O. So given tangents PA, PB from a point P to a circle with central O equal to PB because the lengths of tangents drawn from an external point to a circle are equal. Let us give this as number one. Again we are given the tangents PA and PB from a point P to a circle with central O are inclined to each other at angle of 80 degree. Therefore angle APB is equal to 80 degree. Join OP. Now we know that the tangent at any point of a circle is perpendicular to the radius to the point of contact. So angle OAP is 90 degree and angle OBP is also equal to 90 degree. Right triangles OV have equal to OP common is equal to PB by one. Therefore congruent to triangle OPB equal to angle POB OP by 6. Angle AOV are angle APB. Therefore angle APO is equal to angle BPO. So this implies angle APO is equal to angle BPO is equal to 40 degree as angle APB is 80 degree OA. Angle OAP is 90 degree and angle APO is 40 degree. So we have angle POA is equal to 180 degree minus 90 plus 40 degree and this is equal to 180 degree minus 130 degree which is equal to 50 degree. Hence our option A is correct and this is our answer. I hope the solution is clear to you. Bye and take care.