
Hi! My name is Kerstin. I am in Grade 12 and I am stuck on a problem dealing with Geometry. If you could show me how to get through this problem that would be wonderful! The question is:
"An isoceles triangle has sides measuring 13 cm, 13 cm, and 10 cm. Find the distance from the centroid to the vertex of a base angle."
Thankyou so much!
Hi Kerstin,You can procede in one of two ways.
 Since triangle OSQ is isoceles, it follows that angle ORQ is a right angle and thus from Pythagoras Theorem QR = 12. If you know that the centroid of a triangle is on each of the medians, twothirds of the way from the vertex to the middle of the opposite side, then, in the diagram, PR = 12/3 = 4. Thus you can use the theorem of Pythagoras to find OP.
(In March of 2018 Richard wrote and pointed out an error in my solution to this problem. The error has been fixed. Thanks Richard.)
 Otherwise put a coordinate system on the plane with the origin at O, S at (10,0) and Q at (5,13). Find the coordinates of M, the midpoint of the line segment SQ. Find the coordinates of P, the point where the line joining O to M intersects the line segment joining Q and R. Calculate the distance from O to P.
Cheers,
Harley
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