Select the inscribed circle for the triangle

The option B is correct Inscribe Circle    

Step-by-step explanation:

Given four figure as :

The inscribe circle or in-circle in a triangle is that circle which touches all the three  sided of triangle ,

The circumscribed circle or circum-circle in a triangle is that circle which passes through all the three vertices of triangle

so from the given four figure option B defines the inscribe circle as it touches all the three side of triangle

Hence the option B is correct Inscribe Circle    Answer

B

Step-by-step explanation:

An inscribed circle is the largest possible circle that can be drawn in the interior of a polygon . The inscribed circle is enclosed by another  geometric shape and it is meant to fit .

A circle is usually inscribed in a triangle if the triangle 3 sides are tangent to the circle . The circle inscribed in the triangle is known as an in circle. The center of the incircle is called the incenter. The inscribed circle usually touch the three sides of the triangle.

An inscribed circle of a triangle is the circle that is located or contained in a triangle. The inscribed circle is tangent to the sides of the triangle.

Base on the options only option B fit the explanation of an inscribed circle in a triangle.

< xcy ≅ < xby

step-by-step explanation:

in δcax and δbax,

so, δcax ≅ δbax (side-angle-side or sas)

since δcax ≅ δbax, we can conclude < acx ≅ < abx

in δacy and δaby,

so, δacy ≅ δaby (side-angle-side or sas)

since δacy ≅ δaby, we can conclude < acy ≅ < aby

now,

< acy ≅ < aby

=> < acx + < xcy ≅ < abx + < xby

=> < acx + < xcy ≅ < acx + < xby   (since < acx ≅ < abx already proved above)

subtracting < acx from both sides, we get

< acx + < xcy -< acx ≅ < acx + < xby -< acx

cancelling out < acx and -< acx from both sides, we get

< xcy ≅ < xby (proved)