 Hello and welcome to the session. In this session, we discuss the following question which says, in the given figure, Cp and Cq are tangents to a circle with center o. Arb is another tangent touching the circle at r. If Cp is equal to 11 centimeters and bc is equal to 7 centimeters, then find the length of Br. Let's recon one result which says that the lengths of the two tangents from an external point to a circle are equal. This is the key idea that we use for this question. Let's proceed with the solution now. Consider this figure in which we have Cp and Cq are tangents to a circle with center o. Then this Arb is also a tangent to a circle which touches the circle at the point r. We are given Cp is equal to 11 centimeters, then bc is equal to 7 centimeters and we need to find the length of Br. Now Cp would be equal to Cq as these are the tangents to the circle from the point c and we know that the lengths of the tangents from an external point to a circle are equal. So, we have Cp is equal to Cq. Now, since we have Cp is equal to 11 centimeters, this means that Cq is also equal to 11 centimeters. Now, from the figure you can see that Cq is equal to bc plus bq. We have the length of Cq as 11 centimeters and the length of bc is given as 7 centimeters. So, we substitute bc as 7 and Cq as 11 and from here we get the value of bq as 11 minus 7 which is 4 centimeters. Therefore, we have bq is equal to 4 centimeters. Now, this bq would be equal to Br as these are the tangents to the circle from the point b and we know that the length of the two tangents from an external point to the circle are equal. So, bq is equal to Br. Now, as we have bq is equal to 4 centimeters. So, we get Br is equal to 4 centimeters. So, we get Br equal to 4 centimeters. This is our final answer. So, this completes the session. Hope you have understood the solution of this question.