Question

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

Answer 1

Answer:2.5

Explanation:

Answer 2

2.5cm

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

`Mx^(2) +2.5^(2) =3^(2) \\Mx^(2) =9-6.25\\Mx^(2) =2.75\\Mx=1.65cm`

for triangle BMX

`MB^(2) +1.65^(2) =3^(2) \\MB^(2) +1.65^(2) =3^(2) \\MB^(2) =9-2.75\\\\MB =2.5cm`