Question

Vance wants to construct a circle tangent to all three sides of the acute, scalene triangle LMN using the following steps.

He will draw altitudes from vertex L and vertex M, and mark their intersection point as O.
He will draw the perpendicular from point O to side MN, and mark the intersection point as P.
He will draw the circle centered at point O which will pass through point P.
Which part of Vance's plan requires revision?

A.
Vance should have found the intersection of two perpendicular bisectors of triangle LMN instead of two altitudes.
B.
Vance should have found the intersection of two angle bisectors of triangle LMN instead of two altitudes.
C.
Vance should have used the compass to draw a circle through point N instead of point P.
D.
Vance should have constructed all three altitudes instead of only constructing two altitudes.

Answer 1

Vance should have found the intersection of two angle bisectors of triangle LMN instead of two altitudes.

Step-by-step explanation:

The part of Vance's plan that requires revision is option B: Vance should have found the intersection of two angle bisectors of triangle LMN instead of two altitudes.

When constructing a circle tangent to all three sides of a triangle, the circle should be centered at the incenter of the triangle, which is the intersection point of the angle bisectors of the triangle. The altitudes are not used in constructing this circle.

The correct steps to construct the circle would be to find the intersection of the two angle bisectors of triangle LMN and then draw a circle centered at that intersection point to pass through point P.

Answer 2

B.

Vance should have found the intersection of two angle bisectors of triangle LMN instead of two altitudes.

Step-by-step explanation: