A circle is inscribed in triangle ABC that touches side AB at point C1
| February 18, 2021 | education
A circle is inscribed in triangle ABC that touches side AB at point C1, side BC at point A1, side C A at point B1. Find the perimeter of the triangle if AC1 = 3, BA1 = 5, CB1 = 2.
We use the property of tangents to the circle drawn from one point.
The lengths of tangents drawn to a circle from one point are equal.
Then:
AB1 = AC1 = 3 cm.
CB1 = CA1 = 2 cm.
BC1 = BA1 = 5 cm.
Determine the lengths of the sides of the triangle.
AB = AC1 + BC1 = 3 + 5 = 8 cm.
AC = AB1 + CB1 = 3 + 2 = 5 cm.
BC = BA1 + CA1 = 5 + 2 = 7 cm.
Determine the perimeter of the triangle.
Ravs = AB + AC + BC = 8 + 5 + 7 = 20 cm.
Answer: The perimeter of the triangle is 20 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.
