 to the session. I am Shashi and I am going to help you with the following question. Question says, a tangent PQ at a point P of a circle of radius 5 centimeters meets a line through the center O at a point Q so that OQ is equal to 12 centimeters. The length PQ is a 12 centimeter p 13 centimeters c 8.5 centimeters d square root of 119 centimeters. We have to choose the correct answer here. Let us now start with the solution. First of all, let us draw a simple diagram to represent all the conditions given in the question. Now clearly we can see this is a circle with center O. PQ is a tangent. It touches the circle at point P and we are given that radius of the circle is 5 centimeters so O P is equal to 5 centimeters. L is a line passing through center of the circle and it intersects tangent through P at point Q and we are also given that OQ is equal to 12 centimeters. So we can write we are given with center O a tangent P we are given at radius of a circle that is O P is equal to 5 centimeters and OQ is equal to 12 centimeters. How we will use the theorem which states that that the tangent at any point of a circle is perpendicular to the radius through the point of contact. So we can say O P is perpendicular to PQ here we know O P is the radius PQ is the tangent and P is the point of contact. So the tangent at any point of a circle is perpendicular to the radius through the point of contact. Let us consider triangle O PQ in triangle O PQ you know angle QPO is equal to 90 degrees. So this is a right triangle. Now in right triangle O PQ OQ square is equal to O P square plus PQ square by Pythagoras theorem. So we can write in right triangle O PQ OQ square is equal to O P square PQ square. Now we know OQ is equal to 12 centimeters O P is equal to 5 centimeters. Now substituting corresponding values of O P and O Q in this expression we get 12 square is equal to 5 square plus PQ square 144 is equal to 25 plus PQ square. Now subtracting 25 from both the sides of this expression we get 144 minus 25 is equal to PQ square. Now we know 144 minus 25 is equal to 119. So we get 119 is equal to square of PQ or we can simply write it as PQ square is equal to 119. Now taking square root on both the sides we get PQ is equal to square root of 119. So we can write PQ is equal to root of 119 centimeters. So correct answer is D. This is our required answer. This completes the session. Hope you understood the solution. Take care and have a nice day.