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A circle inscribed in DABC having AB = 10 cm, BC = 12 cm, CA = 28 cm touching sides at D, E, F (respectively). Then AD + BE + CF is ______.
- a)25 cm
- b)20 cm
- c)22 cm
- d)18 cm
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
A circle inscribed in DABC having AB = 10 cm, BC = 12 cm, CA = 28 cm t...
Given:
- A triangle DABC with sides AB = 10 cm, BC = 12 cm, and CA = 28 cm.
- A circle inscribed in the triangle, touching the sides at points D, E, and F.
To find:
The lengths of AD, BE, and CF.
Solution:
To find the lengths of AD, BE, and CF, we need to use the properties of a circle inscribed in a triangle.
Properties of a circle inscribed in a triangle:
1. The point of tangency between the circle and a side of the triangle is the midpoint of that side.
2. The line segment joining the point of tangency and the opposite vertex is perpendicular to the side of the triangle.
3. The lengths of the line segments joining the vertices to the point of tangency are equal.
Let's use these properties to find the lengths of AD, BE, and CF.
Finding AD:
- According to the first property, the point of tangency between the circle and side AB is the midpoint of AB. Let's call this point M.
- Since M is the midpoint of AB, AM = MB = 5 cm.
- According to the third property, the lengths of the line segments joining the vertices to the point of tangency are equal. Therefore, AD = DM = 5 cm.
Finding BE:
- Using the same reasoning as above, we can conclude that BE = EM = 6 cm.
Finding CF:
- Using the same reasoning as above, we can conclude that CF = FM = 14 cm.
Therefore, the lengths of AD, BE, and CF are 5 cm, 6 cm, and 14 cm, respectively. The correct answer is option A, 25 cm.
- A triangle DABC with sides AB = 10 cm, BC = 12 cm, and CA = 28 cm.
- A circle inscribed in the triangle, touching the sides at points D, E, and F.
To find:
The lengths of AD, BE, and CF.
Solution:
To find the lengths of AD, BE, and CF, we need to use the properties of a circle inscribed in a triangle.
Properties of a circle inscribed in a triangle:
1. The point of tangency between the circle and a side of the triangle is the midpoint of that side.
2. The line segment joining the point of tangency and the opposite vertex is perpendicular to the side of the triangle.
3. The lengths of the line segments joining the vertices to the point of tangency are equal.
Let's use these properties to find the lengths of AD, BE, and CF.
Finding AD:
- According to the first property, the point of tangency between the circle and side AB is the midpoint of AB. Let's call this point M.
- Since M is the midpoint of AB, AM = MB = 5 cm.
- According to the third property, the lengths of the line segments joining the vertices to the point of tangency are equal. Therefore, AD = DM = 5 cm.
Finding BE:
- Using the same reasoning as above, we can conclude that BE = EM = 6 cm.
Finding CF:
- Using the same reasoning as above, we can conclude that CF = FM = 14 cm.
Therefore, the lengths of AD, BE, and CF are 5 cm, 6 cm, and 14 cm, respectively. The correct answer is option A, 25 cm.
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Community Answer
A circle inscribed in DABC having AB = 10 cm, BC = 12 cm, CA = 28 cm t...
x + y = 10 cm ... (i)
y + z = 12 cm ... (ii)
x + z = 28cm ... (iii)
Adding (i), (ii) and (iii), we get
2(x + y + z) = 50
x + z = 28cm ... (iii)
Adding (i), (ii) and (iii), we get
2(x + y + z) = 50
⇒ x + y+ z = 25
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A circle inscribed in DABC having AB = 10 cm, BC = 12 cm, CA = 28 cm touching sides at D, E, F (respectively). Then AD + BE + CF is ______.a)25 cmb)20 cmc)22 cmd)18 cmCorrect answer is option 'A'. Can you explain this answer?
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A circle inscribed in DABC having AB = 10 cm, BC = 12 cm, CA = 28 cm touching sides at D, E, F (respectively). Then AD + BE + CF is ______.a)25 cmb)20 cmc)22 cmd)18 cmCorrect answer is option 'A'. Can you explain this answer?, a detailed solution for A circle inscribed in DABC having AB = 10 cm, BC = 12 cm, CA = 28 cm touching sides at D, E, F (respectively). Then AD + BE + CF is ______.a)25 cmb)20 cmc)22 cmd)18 cmCorrect answer is option 'A'. Can you explain this answer? has been provided alongside types of A circle inscribed in DABC having AB = 10 cm, BC = 12 cm, CA = 28 cm touching sides at D, E, F (respectively). Then AD + BE + CF is ______.a)25 cmb)20 cmc)22 cmd)18 cmCorrect answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
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