 Hello and welcome to the session. In this session we discussed the following question which says, find the length of the tangent drawn from a point whose distance from the center of a circle is 25 centimeters given that the radius of a circle is 7 centimeters. Before moving on to the solution, let's discuss one result according to which we have that the tangent at any point of a circle and the radius through this point are perpendicular to each other. This is the key idea that we use for this question. Let's move on to the solution now. According to this figure we have that O is the center of the circle then we have Pt is the tangent to the circle drawn from the point P and it's given that the distance of this point from the center of the circle is 25 centimeters. So this means that Op is equal to 25 centimeters. Also we have that the radius of the circle is 7 centimeters. So this means that Ot is equal to 7 centimeters. Now from the key idea we have that the tangent at any point of a circle and the radius through this point are perpendicular to each other. So according to this key idea Pt would be perpendicular to Ot that is the tangent Pt is perpendicular to the radius Ot since this Pt is the tangent Ot is the radius through the point T and therefore since Pt and Ot are perpendicular we have angle Otp would be equal to 90 degrees that is this angle is of measure 90 degrees. Let us now consider the right triangle Otp in this Op square is equal to Ot square plus Tp square using the Pythagoras theorem. Now we have the values of Op and Ot and we have to find the value of Tp or Pt so substituting the values we have 25 whole square is equal to 7 whole square plus Tp square or you can say Pt square. So further we get Pt square is equal to 25 whole square minus 7 whole square this means Pt square is equal to 625 minus 49 and from here we get Pt square is equal to 576. So Pt is equal to square root of 576 which is equal to 24 and thus we have Pt is equal to 24 centimeters thus the required length of the tangent is equal to 24 centimeters. So this is our final answer. This completes the session. Hope you have understood the solution of this question.