1.

On a circle points a b c are picked on the circumference of the circle. abc form a triangle, such that ab=10, ac=24, bc=26. What is the radius of the circle.Pls help

Answer»

Answer:

13

Step-by-step explanation:

Draw a circle and label three points on the circumference of circle.

Next just check the NUMBERS with pythagoras theorem:

                                          26 ^{2} = 24^{2}  + 10^{2}

                                          LHS = 676

                                          RHS = 576 + 100 = 676

Therefore if the TRIANGLE obey pythagoras theorem, then the angle opposite to the largest side should be right angled. As BC is the largest side angle(A) should be a right angle. Therefore for this to HAPPEN the side bc must be a DIAMETER of the circle  [As diameter makes 180 angle and as per half angle rule the angle subtended at the circumference of a circle must be a right angled if it is subtended from the semicircle(diameter)]. Therefore bc is the diameter(d) of the circle. d=26 therefore radius(r)=26/2=13


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