 Hello and welcome to the session. In this session we are going to discuss the following question and the question says that from this given figure find the radius of the circle. We know that Pythagorean theorem states sum of squares of the length of sites of a right angle triangle is equal to the square of the length of the hypotenuse. That is in a right angle triangle with hypotenuse c and sites a and b we have c square is equal to a square plus b square. With this key idea we shall move on to the solution. In this question we are given a circle on a coordinate plane with a line segment of length 16 units. We have to find the radius of the circle. Now let us label the points on the circle. Here o is the center of the circle. Let this point be m and this point be p such that mp is equal to 16 units and triangle omp is a right angle triangle. We know that any line from center of the circle to the point lying on the circle is equal to radius. So here op and omp are equal and both are the radii of the circle. Also triangle omp is a right angle triangle, right angle at point o. From this figure we see that side mp is the hypotenuse of right angle triangle omp and mp is equal to 16 units and we have to find its radius and let omp is equal to op be equal to x units. So now we have to find the value of x. Now using Pythagoras theorem from the key idea omp square plus op square is equal to mp square that is omp square that is x square plus op square that is also equal to x square is equal to mp square that is 16 square which implies that x square plus x square is 2x square which is equal to 16 square that is 256. which implies that x square is equal to 256 by 2 that is x square is equal to 128. Now taking positive square root on both sides we get x is equal to square root of 128 that is equal to 8 square root of 2 so x is equal to 8 square root of 2 Thus radius of the circle will be equal to 8 square root of 2 units which is a required answer. This completes our session. Hope you enjoyed this session.