The radius of the circle centered at the point O = 10 cm, the length of the chord AB = 16 cm.

| August 7, 2021 | education

The radius of the circle centered at the point O = 10 cm, the length of the chord AB = 16 cm. Find the distance from the chord AB to the parallel to its tangent K.

Let point M be the point of tangency of the circle and tangent K.

Construct the radius of OM to the tangent K, then OM is perpendicular to the tangent.

Since by condition the chord AB is parallel to the tangent line, OH is perpendicular to the chord AB.

We construct the radii OA and OB, then the triangle OAB is isosceles, and OH is its median, then AH = BH = AB / 2 = 16/2 = 8 cm.

In a right-angled triangle AOH, according to the Pythagorean theorem, we determine the length of the leg OH.

OH ^ 2 = OA ^ 2 – AH ^ 2 = 100 – 64 = 36.

OH = 6 cm.

The segment ОМ = R = 10 cm, then НМ = ОМ – ОН = 10 – 6 = 4 cm.

Answer: From chord to tangent 4 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.