 Hello and welcome to the session. Let's work out the following question. It says, construct a tangent to a circle of radius 4 centimeter from a point on the concentric circle of radius 6 centimeter and measure its length. Also verify the measurement by actual calculation. So let's now move on to the solution. We'll do the construction and we'll be writing the steps of construction. The first step is take a point O and draw a circle of radius 4 centimeter. Let the radius be O A and it is of 4 centimeter. So we have drawn a circle with radius 4 centimeter. The second step is with O as center and radius 6 centimeter draw a concentric circle and let the radius be O B which is 6 centimeter. So we have drawn a circle with radius 6 centimeter. Now the third step is draw right by sector of A B and let it intersect O B at C. So we have drawn the right by sector of O B and it intersects O B at C. Now the next step is with C as center and radius OC equal to VC draw a circle to intersect the circle of radius 4 centimeter at P and Q. So we have drawn a circle taking C as center and O B equal to BC OC equal to BC as radius. The next step is join BP and BQ then BP and BQ are the required tangents from the point B on the circle of radius 4 centimeter. So we have joined BP and BQ and BP and BQ are the required tangents. Now if you see the length of BP it would come out to be 4.5 centimeter approximately and similarly the length of BQ would be 4.5 centimeter. Now we will do the actual calculation for justification. If you consider the right triangle BPO since it's a angle in a semi circle therefore it's a right angle triangle where O B is 6 centimeter and O B is 4 centimeter since it's a radius of the circle in right triangle BPO O B is 6 centimeter O B is 4 centimeter therefore O B square O B is the hypotenuse therefore O B square is equal to BP square plus O P square by Pythagoras theorem therefore BP would be equal to O B square minus O P square. Now O B is 6 centimeter so O B square would be 36 and O B square would be 16 that is equal to root 20 which is further equal to 4.47 centimeter approximately that is approximately equal to 4.5 centimeter. Similarly BQ is also 4.5 centimeter as we know that if we draw two tangents from the same point outside the circle the length of the tangents are same so both the tangents have the same length hence justified. So this completes the question and the session. Bye for now. Take care. Have a good day.