 Hello and welcome to the session I am Deepika here. Let's discuss the question which says the length of a tangent from a point A at distance 5 cm from the center of the circle is 4 cm. Find the radius of the circle. We know that a tangent to a circle is a line that intersects the circle at only one point and that common point of the tangent and the circle is called the point of contact. So let's start the solution. We are given a circle with center O. AB is a tangent to the circle. We are given the length of a tangent from a point A at distance center of the circle is 4 cm. We have given OA is equal to 5 cm, AB is equal to 4 cm. We want to find OB. The tangent at any point of a circle is perpendicular to the radius to the point of contact. The tangent at any point of a circle is perpendicular to the radius to the point of contact. Therefore, angle OB A, the tangent at any point of a circle is perpendicular to the radius to the point of contact. Therefore, the tangent to the circle OB is equal to the root of OA square minus therefore OB is equal to is equal to the root of 25 minus 16 and this is again equal to under root of 9 which is equal to 3. OB is equal to 3 cm. Hence the radius of the circle is 3 cm and this is our answer. I hope the solution is clear to you. Bye. Take care.