Two circles touch each other internally. Their radii are 4cm and 6cm. The length of the largest chord of the outer circle, if this chord lies outside the smaller circle will be :

To find the length of the largest chord of the outer circle, we can use the concept of tangents and chords.

Step 1: Draw the two circles, one with a radius of 4cm and the other with a radius of 6cm. Make sure they touch each other internally.

Step 2: Draw a line connecting the centers of the two circles. This line will be the common tangent to both circles.

Step 3: Extend the line beyond the larger circle until it intersects the circumference of the larger circle. This point of intersection will be one end of the largest chord.

Step 4: Draw a line from the center of the larger circle to the point of intersection on the circumference. This line will be the radius of the larger circle.

Step 5: Now, we have a right-angled triangle formed by the radius of the larger circle, the line connecting the centers of the two circles, and the line from the center of the larger circle to the point of intersection on the circumference.

Step 6: Use the Pythagorean theorem to find the length of the line connecting the centers of the two circles. The formula is a^2 + b^2 = c^2, where a and b are the lengths of the two shorter sides of the triangle, and c is the length of the hypotenuse.

Step 7: Substitute the values into the formula. In this case, a = 4cm and b = 6cm. Solve for c.

Step 8: Once you have the length of the line connecting the centers of the two circles, double it to get the length of the largest chord of the outer circle.

Step 9: The final answer will be the length of the largest chord of the outer circle when it lies outside the smaller circle.

To find the length of the largest chord of the outer circle, we can use the concept of tangents and chords.

Step 1: Draw the two circles, one with a radius of 4cm and the other with a radius of 6cm. Make sure they touch each other internally.

Step 2: Draw a line connecting the centers of the two circles. This line will be the common tangent to both circles.

Step 3: Extend the line beyond the larger circle until it intersects the circumference of the larger circle. This point of intersection will be one end of the largest chord.

Step 4: Draw a line from the center of the larger circle to the point of intersection on the circumference. This line will be the radius of the larger circle.

Step 5: Now, we have a right-angled triangle formed by the radius of the larger circle, the line connecting the centers of the two circles, and the line from the center of the larger circle to the point of intersection on the circumference.

Step 6: Use the Pythagorean theorem to find the length of the line connecting the centers of the two circles. The formula is a^2 + b^2 = c^2, where a and b are the lengths of the two shorter sides of the triangle, and c is the length of the hypotenuse.

Step 7: Substitute the values into the formula. In this case, a = 4cm and b = 6cm. Solve for c.

Step 8: Once you have the length of the line connecting the centers of the two circles, double it to get the length of the largest chord of the outer circle.

Step 9: The final answer will be the length of the largest chord of the outer circle when it lies outside the smaller circle.