Question

Assertion :Statement 1: In $\Delta ABC,$ the centroid $\left(G\right)$ divides the line joining orthocenter $\left(H\right)$ and circucenter in ratio $2:1$. Reason: Statement 2: The centroid $\left(G\right)$ divides the median $AD$ in ratio $2:1$.

• A. Both the statements are TRUE and STATEMENT 2 is the correct expansion of STATEMENT 1
• B. Both the statements are TRUE but STATEMENT 2 is NOT the correct explanation of STATEMENT 1
• C. STATEMENT 1 is TRUE and STATEMENT 2 is FALSE
• D. STATEMENT 1 is FALSE and STATEMENT 2 is TRUE

Answer 1

The correct option is B Both the statements are TRUE but STATEMENT 2 is NOT the correct explanation of STATEMENT 1

Statement 1: In $\Delta$ ABC, the centroid $\left(G\right)$ divides the line joining orthocenter $\left(H\right)$ and circumcenter in ratio $2:1$.

Statement 2: The centroid $\left(G\right)$ divides the median $AD$ in ratio $2:1$.

Both the statement are true but statement $2$ is not the correct explanation of statement $1$, because its not necessary the orthocenter $\left(H\right)$ and circumcenter $\left(C\right)$ will lie of median $AD$ also orthocenter is the point of intersection of attitudes from each vertex and circumcenter is the point of intersection of bisectors of each sides of a triangle.So its not necessary that they all be lying on the median.