Q1 of 24 Page 283

Let us write what is the length of circum radius of a triangle lengths of sides of which are 6 cm, 8 cm and 10 cm.


1.JPG


The Δ PQR is right angled at Q


Let PQ = 8 cm


QR = 6 cm


PR = 10 cm


Squaring and adding the smaller two sides of the triangle we get


PQ2 + QR2 = 62 + 82


PQ2 + QR2 = 36 + 64


⇒ PQ2 + QR2 = 100


⇒ PQ2 + QR2 = 102


⇒ PQ2 + QR2 = PR2


So we see the sum of squares of the two smaller sides is equal to the square of the larger side.


Hence the triangle is a right angled triangle.


The circum radius of a right angled triangle is always half of the length of the hypotenuse.


Circum radius


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