 Hello and welcome to this session. In this session we will discuss a question which says that two concentric circles are of radii 8 cm and 10 cm. Find the length of the cord of the larger circle which touches the smaller circle. Now before starting the solution of this question, you should know some results. And that are perpendicular drawn from the center of the circle is perpendicular to the point of conduct. Now these results will represent as a key idea for solving this question. And now we will start the solution. Now here it is given two concentric circles with center o. And here the radius of the inner circle which is oe is equal to 8 cm. And the radius of the outer circle is ob which is equal to 10 cm. The length of the cord of the larger circle which is bd which is touching the inner circle at the point o. So given the radius of the inner circle which is oe is equal to 8 cm. The radius of the outer circle which is ob is equal to 10 cm. And we have to find the length of the cord of the larger circle that is bd. Now using the second result which is given in the key idea, ab will be equal to 90 degrees. So angle oeb is equal to 90 degrees because tangent is perpendicular to the radius through the point of conduct. As oe is the radius and bd which is the cord of the larger circle is tangent to the inner circle at the point a. Now in triangle ab since oeb is the right angle triangle. So by Pythagorean theorem oe square is equal to oe square plus ab square. Which implies oe which is 10 cm. So it will be 10 square is equal to oe which is 8 cm. So oe square will be 8 square plus ab square. This implies 100 is equal to 64 plus ab square. Which further implies ab square is equal to 100 minus 64. This further implies ab square is equal to 36. Which implies ab is equal to 6 cm. Now using the first result which is given in the key idea. The pentagonal drum from the center of the circle to the cord bisects the cord. Now we can rise perpendicular to bd. Therefore the circle sets bd. This means we can be written as ab is bd is equal to as ab is equal to ab which is root area. So this will be equal to ab plus ab. Which implies bd is equal to 2 into ab. Now we have 6 cm. bd is equal to 2 into 6 cm which is equal to 12 cm. The length of the cord that is bd is equal to 12 cm. That's all for this session. Hope you all have enjoyed the session.