# The circle centered on side AC of triangle ABC passes through vertex C and touches line AB at point B.

December 29, 2020 | education

| **The circle centered on side AC of triangle ABC passes through vertex C and touches line AB at point B. Find the diameter of the circle if AB = 15, AC = 25.**

Let’s draw the segment OB to the point of tangency of the circle. Since AB is tangent, the angle OBA is rectangular.

In the VOS triangle, the OB and OS segments are equal to the radius of the circle. Since, by condition, the length of the segment AC = 25 cm, then the length of the segment OA = AC – OC = 25 – R.

In a right-angled triangle AOB, by the Pythagorean theorem, we define the leg OB.

ОВ2 = ОА2 – АВ2.

R2 = (25 – R) 2 – 152.

R2 = 625 – 50 * R + R2 – 225.

50 * R = 400.

R = 400/50 = 8 cm.

Then D = 2 * R = 16 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.