Question

Given circle M with diameter KL and radius MI. IJ is tangent to M at I. If MI = 14 and IJ = 40, solve for MJ. Round your answer to the nearest tenth if necessary. If the answer cannot be determined, click "Cannot be determined."

Answer 1

To solve for MJ, we apply the Pythagorean theorem to the right triangle formed by the radius MI, the tangent IJ, and the hypotenuse MJ. With MI = 14 and IJ = 40, we find that MJ is approximately 42.4 units.

Step-by-step explanation:

You are asked to solve for MJ in a geometrical situation involving a circle with a diameter and a tangent line. Given that MI is the radius of the circle M and equals 14, and IJ is the tangent to the circle at point I with a length of 40, we can use the Pythagorean theorem to find the length of MJ. Since MI is a radius and MJ is a hypotenuse in a right-angled triangle MIJ, we have:

MJ2 = MI2 + IJ2

Substituting the given values yields:

MJ2 = 142 + 402

MJ2 = 196 + 1600

MJ2 = 1796

Taking the square root of both sides gives:

MJ = √1796 ≈ 42.4

Therefore, the length of MJ is approximately 42.4 units, rounded to the nearest tenth.