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In a triangle ABC, the lengths of the sides AB and AC equal 17.5 cm and 9 cm respectively. Let D be a point on the segment BC such that AD is perpendicular to BC. If AD = 3 cm, then what is the radius (in cm) of the circle circumscribing the triangle ABC?
- a)17.05
- b)27.85
- c)22.45
- d)26.25
Correct answer is option 'D'. Can you explain this answer?
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In a triangle ABC, the lengths of the sides AB and AC equal 17.5 cm an...
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In a triangle ABC, the lengths of the sides AB and AC equal 17.5 cm an...
Given information:
- Length of side AB = 17.5 cm
- Length of side AC = 9 cm
- Length of AD = 3 cm
Calculating the length of side BC:
- Using Pythagorean theorem in triangle ABC,
- AB^2 = AC^2 + BC^2
- 17.5^2 = 9^2 + BC^2
- BC^2 = 306.25 - 81
- BC^2 = 225
- BC = 15 cm
Calculating the radius of the circumcircle:
- The circumcircle of a triangle is the circle passing through all three vertices.
- The radius of the circumcircle can be found using the formula R = (abc)/(4A), where a, b, c are the sides of the triangle and A is the area of the triangle.
- First, we calculate the area of the triangle using Heron's Formula:
- s = (AB + AC + BC)/2 = (17.5 + 9 + 15)/2 = 20.25 cm
- Area (A) = √(s(s-AB)(s-AC)(s-BC)) = √(20.25*3.75*11.25*5.25) = 33.75 cm^2
- Now, calculate the radius of the circumcircle:
- R = (AB*AC*BC)/(4A) = (17.5*9*15)/(4*33.75) = 26.25 cm
Therefore, the radius of the circle circumscribing triangle ABC is 26.25 cm, which corresponds to option 'D'.
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In a triangle ABC, the lengths of the sides AB and AC equal 17.5 cm and 9 cm respectively. Let D be a point on the segment BC such that AD is perpendicular to BC. If AD = 3 cm, then what is the radius (in cm) of the circle circumscribing the triangle ABC? a)17.05b)27.85c)22.45d)26.25Correct answer is option 'D'. Can you explain this answer?
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