Question

Assertion
Statement 1: In triangle ABC, the centroid (G) divides the line joining orthocentre (O) and circumcentre (C) in ratio 2 : 1.
Reason
Statement 2: The centroid (G) divides the median AD in ratio 2 : 1. Select the correct option:
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

Hint: Use the fact that the centroid (G) of any triangle ABD divides the line joining orthocentre (O) and circumcentre (C) in ratio 2 : 1. Also, that the centroid (G) divides the median AD in ratio 2 : 1.

Complete step-by-step answer:
In the question, we have to check that the Statement 1: In triangle ABC, the centroid (G) divides the line joining orthocentre (O) and circumcentre (C) in ratio 2 : 1, is true or not and also we have to check that Statement 2: The centroid (G) divides the median AD in ratio 2 : 1, is correct or not. Finally, we have to check if statement 2 is the explanation of statement 1 or not.
So, here we know that In triangle ABC, the centroid (G) divides the line joining orthocentre (O) and circumcentre (C) in ratio 2 : 1. Also, we know that The centroid (G) divides the median AD in ratio 2 : 1. But the explanation given in statement 2 is not the correct reason for the statement 1 to be true.
So, from this we can say that option B, which says that Both the statements are TRUE but STATEMENT 2 is NOT the correct explanation of STATEMENT 1 is the correct answer.
Hence, option B is the correct answer.

Note: It can be noted that the centroid (G), orthocentre (O) and circumcentre (C) lies in the straight line and hence are collinear. But it is not to be confused that this straight line will be the median of the triangle. So the straight line is the Euler line and not the median.