confusing explanation (Question:133328.0)

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gaurav prajapati

· started a discussion

· 1 Months ago

confusing explanation (Question:133328.0)

if o is the circum centre then how PM could be circum radius

Question:

If in the given figure, ∠PQR = 90°, O is the centroid of ∆PQR, PQ = 5cm and QR = 12cm, then OQ is equal to:

Options:

3.33 12 $\frac{1}{2}$

4.33 13 $\frac{1}{3}$

4.50 12 $\frac{1}{2}$

5.33 13 $\frac{1}{3}$

Solution:

By Pythagoras theorem,

PR²=PQ²+QR²

PR=13cm

∵ O is the centroid ⇒ QM is median

∵ PQR is a right angle triangle and M is mid point of PR,

Hence O is Circumcentre

∴ PM = MR = QM ( circum radius )

∴ QM = PM = (13/2)cm

∵ centroid divides median in ratio = 2:1

∴ OQ =(2/3)QM

=(2/3)×(13/2)= 4.33cm

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