A tangent AB (B is a tangency point) and a secant line intersecting the circle C and K are drawn through
| September 25, 2021 | education
A tangent AB (B is a tangency point) and a secant line intersecting the circle C and K are drawn through point A so that AC = 4cm, AK = 16. find the length AB.
Let us construct a segment BK and prove the similarity of triangles ABC and ABK.
In triangles ABC and ABK, angle A is common. The angle ABC formed by the chord and the tangent is equal to half of the arc BC, and the inscribed angle of the KPM is also equal to half of the arc BC on which it rests, then the angle ABC = AKB, and the triangles ABC and ABK are similar in two angles.
Then in similar triangles: AB / AK = AC / AB.
AB ^ 2 = AK * AC = 16 * 4 = 64.
AB = 8 cm.
Answer: The length of the segment AB is 8 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.
