in a right triangle abc,right-angled at b,bc=12cm and ab=5cm.the radius of the circle inscribed in the inscribed in the triangle(in cm) is
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In triangle ABC
∠B=90° and AB=5 cm and BC=12 cm
According to Pythagoras theorem
(AC)²=(AB)² + (BC)²
AC=√(5)² + (12)²
AC=13 cm
Let the center of the circle be O and the radius be x
Construction: Join OA, OB and OC
We know that the tangent to a circle always makes an angle of 90°
Area of ABC= 1/2 × base × height
= 1/2 ×12 × 5 = 30 cm²
Area of ABC= ar.OAB+ ar.OBC+ ar.OAC
30 cm²= 1/2*x*5 + 1/2*x*12 +1/2*x*13
30 cm²= (5x/2 + 12x/2 + 13x/2) cm²
30 cm² × 2= 5x+12x+13x
60 cm²= 30x
x= (60/30) cm²
x= 2 cm
∴ the radius is 2 cm
∠B=90° and AB=5 cm and BC=12 cm
According to Pythagoras theorem
(AC)²=(AB)² + (BC)²
AC=√(5)² + (12)²
AC=13 cm
Let the center of the circle be O and the radius be x
Construction: Join OA, OB and OC
We know that the tangent to a circle always makes an angle of 90°
Area of ABC= 1/2 × base × height
= 1/2 ×12 × 5 = 30 cm²
Area of ABC= ar.OAB+ ar.OBC+ ar.OAC
30 cm²= 1/2*x*5 + 1/2*x*12 +1/2*x*13
30 cm²= (5x/2 + 12x/2 + 13x/2) cm²
30 cm² × 2= 5x+12x+13x
60 cm²= 30x
x= (60/30) cm²
x= 2 cm
∴ the radius is 2 cm
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