Question
Find the length of AC in right angled triangle ABC which has a circle inscribed in it, that touches the sides AB, BC and CA at D, E and F respectively, and has AD = 6 cm and BE = 5 cm.
Find the length of AC in right angled triangle ABC which has a circle inscribed in it, that touches the sides AB, BC and CA at D, E and F respectively, and has AD = 6 cm and BE = 5 cm.
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Solution
The correct option is D 61 cm
AD = AF = 6 cm; BD = BE = 5 cm; EC = FC = x.
Applying Pythagoras theorem,
AC2=BC2+AC2 i.e., 121+(5+x)2=(6+x)2
Solving, we get x = 55.
AC = 55 + 6 = 61 cm
AD = AF = 6 cm; BD = BE = 5 cm; EC = FC = x.
Applying Pythagoras theorem,
AC2=BC2+AC2 i.e., 121+(5+x)2=(6+x)2
Solving, we get x = 55.
AC = 55 + 6 = 61 cm
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