Answer:
2.5cm
Step-by-step explanation:
Point X is the circumcenter of ΔABC. Point X is the circumcenter of triangle A B C. Lines are drawn from each point of the triangle to point X. The lengths of the line segments are 3 centimeters. Lines are drawn from point X to the sides of the triangles to form right angles and line segments X M, X N, and X L are formed. The length of L A is 3 centimeters, the length of A M is 2.5 centimeters, and the length of N B is 2 centimeters. What is the length of MB? 1.5 cm 2 cm 2.5 cm 3 cm
From pythagoras principle that says for a right angle traingle, the square of hypotenuse is equal to the square of the adjacent and the square of the opposite side of the right angle triangle.
We draw a triangle ABC, draw a line to the x, circumcenter
draw a line to the side of the triangle
considering triangle AMX, applying pythagoras rule
[tex]Mx^{2} +2.5^{2} =3^{2} \\Mx^{2} =9-6.25\\Mx^{2} =2.75\\Mx=1.65cm[/tex]
for triangle BMX
[tex]MB^{2} +1.65^{2} =3^{2} \\MB^{2} +1.65^{2} =3^{2} \\MB^{2} =9-2.75\\\\MB =2.5cm[/tex]
