Chord MN and PK intersect at point E so that ME = 12cm, NE = 3cm, PE = KE. Find PK

Let’s connect the points K and P, and K and N.

Consider triangles MEP and KEN, which are similar in two angles. The angle MEP is equal to KEN, as are the vertical angles. Angle PMN = PKN as supported by one arc PN.

In a similar triangle: MP / PE = KE / NE.

MR * NE = PE * KE = PE ^ 2.

12 * 3 = 36 = PE ^ 2.

PE = 6 cm.

RK = 2 * PE = 12 cm.

Answer: The length of the RK chord is 12 cm.

One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.