 Hello and welcome to the session. I am Deepika here. Let's discuss a question which says in given figure xy and x dash y dash are two parallel tangents to a circle with center o and the tangent ab with point of contact c intersecting xy at a and x dash y dash at b prove that angle a o b is equal to 90 degree. Now we know that the lengths of a circle are equal. So this is the key idea behind that question. We will take the help of this key idea to solve the above question. So let's start the solution. Now we are given parallel tangents xy and x dash y dash to a circle with center o and q are the points of contact of tangents xy and x dash y dash respectively. ab is another tangent with point of contact c intersecting xy at a and x dash y dash at b. ab is equal to 90 degree construction and oc pa tangents to the circle from an external point a. Therefore a is equal to ca because according to our key idea lengths of tangents drawn from an external point to a circle are equal. Interangle pa o triangle ca o or aoc we have a is equal to ac proved above oa is equal to oa common is equal to oc radii of the same circle. Therefore triangle pa o is congruent to triangle aoc by sss congruency condition a o a o is equal to angle ca o by c p c t. Now angle pa c is equal to angle pa o plus angle ca o or we can write angle pa c is equal to twice angle ca o because angle pa o is equal to angle ca o. Similarly, in triangle qob and triangle boc we have the qbo equal to angle cpo. Therefore angle qbc is equal to twice angle cbo. As number one and this is number two now xy dash y dash therefore angle pa angle qbc is equal to 180 degree. These are the sum of the interior angles on the same side of the transversal implies twice angle ca o plus twice angle cbo is equal to 180 degree using one length two. This implies angle ca o plus angle cbo is equal to 90 degree. Let us give this as number three. Now in triangle ob we have angle ba o or angle ca o bo or angle cbo the aob is equal to 180 degree. Angle sum property of a triangle this implies 90 degree plus angle aob is equal to 180 degree using three because in three we have angle ca o plus angle cbo is equal to 90 degree. This implies angle aob is equal to 180 degree minus 90 degree and this is equal to 90 degree. Hence we have proved that angle aob is equal to 90 degree hence proved. I hope the solution is clear to you. Bye and take care.