A circle of radius 3 cm is drawn inscribed in a right angle triangle ABC, right angled at C. If AC is 10 Find the value of CB *
Answers
Given : A circle of radius 3 cm is drawn inscribed in a right angle triangle ABC, right angled at C
AC = 10 cm
To Find : CB
Solution:
AC = 10 cm
CB = x cm
AB =√AC² + CB² = √10² + x² = √(x² + 100)
radius = cm
Area of Δ ABC = (1/2) AC * CB
= (1/2)10*x
= 5x cm²
Area of Δ ABC = (1/2) (AC + CB + AC) * r
= (1/2)(10 + x + √(x² + 100)) * 3
(1/2)(10 + x + √(x² + 100)) * 3 = 5x
=> 30 + 3x + 3√(x² + 100) = 10x
=> 3√(x² + 100) = 7x - 30
Squaring both sides
=> 9(x² + 100) = 49x² - 420x + 900
= 40x² = 420x
=> x = 420/40
=> x = 21/2
=> x = 10.5 cm
CB= 10.5 cm
value of CB = 10.5 cm
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