In figure a right angled triangle ABC circumscribe a circle of radius r. If AB and BC are of length 8cm and 6cm respectively find the value of r
Answers
Given : a right angled triangle ABC circumscribe a circle of radius r
AB = 8 cm BC = 6 cm
To Find : value of r
Solution:
Pythagoras' theorem: square on the hypotenuse of a right-angled triangle is equal to the sum of the squares of the other two perpendicular sides.
AB = 8 cm BC = 6 cm
AC² = AB² + BC²
=> AC² = 8² + 6²
=> AC² = 64 + 36
=> AC² = 100
=> AC = 10
Area of triangle = (1/2) * AB * BC
Area of Triangle = (1/2)(AB + BC + AC) * r
(1/2) * AB * BC = (1/2)(AB + BC + AC) * r
=> 8 * 6 = (8 + 6 + 10) * r
=> 48 = 24r
=> r = 2
value of r = 2 cm
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ANSWER :
Given,
- A right angled triangle ABC circumscribe a circle of radius r.
- Length of AB = 8 cm.
- Length of BC = 6 cm.
To Find,
- Find the value of r.
Solution,
Applying Pythagoras Theorem,
AC² = AB² + BC²
→ AC² = 8² + 6²
→ AC² = 64 + 36
→ AC² = 100
→ AC = 10
Area of triangle = (1/2) × AB × BC
Area of triangle = (1/2)(AB + BC + AC) × r
(1/2) × AB × BC = (1/2)(AB + BC + AC) × r
→ 8 × 6 = (8 + 6 + 10) × r
→ 48 = 24r
→ r = 48/24
→ r = 2