 Hello and welcome to the session. The given question says, in figure 2, Pt is equal to 6 centimeters, AB is equal to 5 centimeters by the length of PA. Let's start with the solution. So, here we are given that the length of the tangent from the point P to the circle is 6 centimeters and also we are given that AB is equal to 5 centimeters and we have to find PA. Now we know that if PAB is a secant to a circle intersecting at points A and B and Pt is a tangent to the circle then Pb is equal to Pt square which is by theorem 10.2 of your book. So, here let us take PA is equal to x centimeters. So, on substituting the values here we have PA is equal to x into Pb is x plus 5 t square and Pt is 6. So, this is for the equal to x square plus 5x is equal to 36 or we have x square plus 5x minus 36 is equal to 0. Now, by splitting the middle term it can further be written as x square plus 9x minus 4x minus 36 is equal to 0. Taking x common from the first two terms and minus 4 common from the last two terms we have x into x plus 9 minus 4 into x plus 9 is equal to 0 which further implies that x minus 4 into x plus 9 is equal to 0. Now, we know that if the product of two numbers is equal to 0 then at least one of them is 0 that is either A is equal to 0 or we have B is equal to 0 right. So, from here we can say that either x minus 4 is equal to 0 or x plus 9 is equal to 0. So, we have x is equal to 4 or minus 9. Now, the length cannot be negative therefore x is equal to minus 9 we will reject and we have x is equal to 4 that is the length of P a is equal to 4 centimeters. So, this completes the session by intake queue.