question_answer

In the given figure \[{{270}^{o}}\], O is the centroid of \[{{60}^{o}}\] PQ = 5 cm and QR = 12 cm, then OQ is equal to:

A)  \[{{300}^{o}}\]                              

B)  \[{{240}^{o}}\]

C)  \[{{120}^{o}}\]                  

D)  \[{{120}^{o}}\]

Correct Answer: B

Solution :

Given: PQ = 5 cm, QR= 12 cm and \[\angle A-\angle C={{0}^{o}}\] \[x+10\] We can draw a circle which is passing through points P, Q and R such that PM = MR = QM Now,  \[\angle CBP\] \[{{105}^{o}}\]   (By Pythagoras theorem) Since, 0 is the centroid \[{{115}^{o}}\] QM is the Median. Now, QM is Median \[{{135}^{o}}\] \[\Delta ABC\] Since, \[\angle BAC\] \[\angle ECD={{30}^{o}}\] \[\angle BAC\] Now, centroid divides median in 2 : 1 \[{{30}^{o}}\] \[{{40}^{o}}\]