# In a triangle MNK MN = 6cm, MK = 8cm, NK = 10cm. Prove that an MK-segment is a tangent line drawn from point K

December 29, 2020 | education

| **In a triangle MNK MN = 6cm, MK = 8cm, NK = 10cm. Prove that an MK-segment is a tangent line drawn from point K to a circle centered at point N and radius 6cm.**

Let MK be a segment of the tangent to the circle centered at point N.

Then, since the tangent to the circle is perpendicular to the radius, the MNK triangle is rectangular, with a radius of MN = 6 cm.

Let us check this using the Pythagorean theorem.

MN = ((NK) ^ 2 – (MK) ^ 2) ^ (1/2) = (10 ^ 2 – 8 ^ 2) ^ (1/2) = (100 – 64) ^ (1/2) = 6 cm.

Thus, MN = 6 cm is the radius, and MK is the segment of the tangent to the circle with the center at point N.

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