The distance from point A to the center of the circle is less than the radius of the circle.
| September 20, 2021 | education
The distance from point A to the center of the circle is less than the radius of the circle. Prove that any line passing through point A is a secant with respect to the given circle.
Draw straight C through point A.
From point O, the center of the circle, we construct the height OH.
Triangle AON is rectangular, then, according to the Pythagorean theorem, OH² = OA² – AH².
OH = √ (OA² – AH²).
By hypothesis, ОА <R, and then ОН <R.
Since OH <R, then the line C intersects the circle at two points, and therefore is a secant, which was required to be proved.
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.
