Triangle Centers - Problem Solving Practice Problems Online

Let $A=(2,12)$ , $B=(10,0)$ and $O=(0,0)$ be the vertices of triangle $AOB.$ If $G$ is the centroid of the triangle, what are the coordinates of $G$ and the area of triangle $AGB ?$

G=(4,4), \triangle AGB={20}

G=(4,6), \triangle AGB={20}

G=(4,4), \triangle AGB={40}

G=(4,6), \triangle AGB={40}

Point $O$ is the circumcenter of $\triangle {ABC}$ . If $\angle AOB : \angle BOC : \angle COA = 2:3:4,$ what is the measure of $\angle BAC$ ?

90^\circ

30^\circ

45^\circ

60^\circ

Triangle $ABC$ has incenter $I$ . Let the incircle be tangential to sides $AB, BC,$ and $CA$ at points $F,D,$ and $E,$ respectively. If the lengths of $BC, CA,$ and $AB$ are $19日,22日$ and $23,$ respectively, what is the length of $AF$ ?

$A=(17,4)$ is a vertex of triangle $ABC$ and $O=(0,0)$ is its circumcenter. $P, Q$ and $R$ are the midpoints of sides $AB, BC$ and $CA,$ respectively. If the orthocenter of triangle $PQR$ is $H,$ then what is the equation of line $AH?$

y=\frac{4}{17}x

y={21}x

y={4}x

y={17}x

$ABC$ is an acute angle triangle with points $D$ and $E$ on $BC$ and $AC$ , respectively, such that $BE$ and $AD$ are altitudes. $AD$ and $BE$ intersect at $H$ . If $\angle BCA = 42 ^\circ$ and $\angle EBA = 2 \angle DAB$ , what is the measure of $\angle ABC$ (in degrees)?

Details and assumptions:
- $H$ is also known as the orthocenter of the triangle, which is the intersection point of all 3 altitudes.

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Triangle Centers - Problem Solving