Two triangles DEF and XYZ are congruent to each other such that DE = 10 cm, YZ = 24 cm, and ∠DEF = ∠XYZ = 90⁰. Find the circumradius of ΔDEF.
According to the question: If two triangles are congruent to each other, then their corresponding sides and angles are equal. We have, ΔDEF ≅ ΔXYZ. So, EF = YZ = 24 cm. ΔDEF is a right-angled triangle. So, by the Pythagorean theorem: DF² = DE² + EF². So, DF² = 10² + 24². Or, DF² = 100 + 576 = 676. Or, DF = 26. But length cannot be negative. So, DF = 26 cm. Now, the circumradius of a right-angled triangle = (hypotenuse/2). So, the circumradius of ΔDEF = (26/2) = 13 cm.
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