AB is the diameter of the circle with the center O, M is the point of this circle.
| February 18, 2021 | education
AB is the diameter of the circle with the center O, M is the point of this circle. Find the perimeter of the triangle MOB, if it is known that AB = 13, AM = 12.
If one of the sides of a triangle inscribed in a circle is equal to the diameter of the circle, then this triangle is rectangular, and the diameter is the hypotenuse of this triangle.
Determine the length of the leg AM of the right-angled triangle AMB.
By the Pythagorean theorem AB ^ 2 = BM ^ 2 + AM ^ 2.
BM ^ 2 = AB ^ 2 – AM ^ 2 = 169 – 144 = 25.
VM = 5 cm.
Segments ОМ and ОВ are the radii of the circle, and, accordingly, are equal to each other.
AB is the diameter of the circle, then OM = OB = AB / 2 = 13/2 = 6.5 m.
Then Рmov = ОВ + ОМ + MB = 6.5 + 6.5 + 5 = 18 cm.
Answer: Rmov = 18 cm.
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