 Hello and welcome to the session. Let us discuss the following question. It says in figure 2, P a is 3 cm, A b is 9 cm, C d is 5 cm. Find the length of P c. So let's now move on to the solution. We are given that P a is 3 cm, A b is 9 cm, C d is 5 cm and we have to find the length of P c. So let P c be equal to x cm. Now if P c is x cm, therefore P d will be equal to x plus 5 cm. That is P d is equal to P c plus C d. Now we know that P b into P a is equal to P d into P c. Let's now substitute all these values. Now P b is 3 plus 9 cm into P a which is 3 cm is equal to P d which is x plus 5 cm into P c which is x. It is not 19, it is 9. Now 9 plus 3 is 12. So it is 12 into 3 is equal to x into x is x square plus x into 5 is 5x. So this implies x square plus 5x is equal to 36. So this implies x square plus 5x minus 36 is equal to 0. Now we will factorize this quadratic equation. So we will have x square plus 9x minus 4x minus 36 is equal to 0 taking x common from the first two terms we have x into x plus 9. Now taking minus 4 common from the last two terms we have minus 4 into x plus 9 is equal to 0. Now taking x plus 9 common we have x plus 9 into x minus 4 is equal to 0. So this implies x plus 9 is equal to 0 or x minus 4 is equal to 0. So this implies x is equal to minus 9 or x is equal to 4. But since x is the length of P c it cannot be negative. So x is equal to minus 9 is rejected. So we have x is equal to 4. Therefore P c is 4 centimeter. So this completes the question. For this question do remember this result if two chords of the circle intersect inside or outside the circle then the rectangle formed by two parts of the chord, two parts of the one chord is equal to the area of the rectangle formed by the two parts of the other chord. And this is very important property. So do write this property while solving such questions. So bye for now. Take care. Have a good day.