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In a right angle triangle ABC with vertex B being the right angle, the mutually perpendicular sides AB and BC are p cm and q cm long respectively. If the length of the hypotenuse is (p + q — 6)cm, the radius of the largest possible circle that can be inscribed in the triangle is
- a)1.5 cm
- b)3 cm
- c)6 cm
- d)3.3 cm
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
In a right angle triangle ABC with vertex B being the right angle, th...
To find the radius of the largest possible circle that can be inscribed in a right-angled triangle, we need to apply some geometry principles.
Let's consider the given right-angled triangle ABC, where B is the right angle. The mutually perpendicular sides AB and BC are p cm and q cm long, respectively. The length of the hypotenuse is given as (p - q - 6) cm.
We can start by drawing the triangle and labeling the sides and angles to better visualize the problem.
Now, let's proceed with the solution step-by-step:
1. Finding the length of the hypotenuse:
Given: Hypotenuse = (p - q - 6) cm
2. Applying the Pythagorean theorem:
According to the Pythagorean theorem, in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. In this case, we have:
(p - q - 6)^2 = p^2 + q^2
3. Expanding the equation:
p^2 - 2pq + q^2 - 12p + 12q + 36 = p^2 + q^2
4. Simplifying the equation:
-2pq - 12p + 12q + 36 = 0
-2pq + 12q = 12p - 36
2pq - 12q = -12p + 36
2q(p - 6) = -12(p - 3)
2q = -12
q = -6
5. Identifying the problem:
We have obtained a negative value for q, which is not possible in this context. Therefore, there is no valid solution for this problem.
6. Conclusion:
Since we cannot find a valid solution for the given triangle, we cannot determine the radius of the largest possible circle that can be inscribed in it.
Thus, none of the given options (A, B, C, or D) is the correct answer.
Let's consider the given right-angled triangle ABC, where B is the right angle. The mutually perpendicular sides AB and BC are p cm and q cm long, respectively. The length of the hypotenuse is given as (p - q - 6) cm.
We can start by drawing the triangle and labeling the sides and angles to better visualize the problem.
Now, let's proceed with the solution step-by-step:
1. Finding the length of the hypotenuse:
Given: Hypotenuse = (p - q - 6) cm
2. Applying the Pythagorean theorem:
According to the Pythagorean theorem, in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. In this case, we have:
(p - q - 6)^2 = p^2 + q^2
3. Expanding the equation:
p^2 - 2pq + q^2 - 12p + 12q + 36 = p^2 + q^2
4. Simplifying the equation:
-2pq - 12p + 12q + 36 = 0
-2pq + 12q = 12p - 36
2pq - 12q = -12p + 36
2q(p - 6) = -12(p - 3)
2q = -12
q = -6
5. Identifying the problem:
We have obtained a negative value for q, which is not possible in this context. Therefore, there is no valid solution for this problem.
6. Conclusion:
Since we cannot find a valid solution for the given triangle, we cannot determine the radius of the largest possible circle that can be inscribed in it.
Thus, none of the given options (A, B, C, or D) is the correct answer.
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Community Answer
In a right angle triangle ABC with vertex B being the right angle, th...
The largest possible circle that can be inscribed in the triangle is the one which touches the 3 sides. Since A is an external point from where AN and AM are tangents to this circle, we have AM = AN = a (say)
CN=CL=b (say)
If O is the centre of the circle, then OM = OL = r (radius of this circle)
BC = q = b + r and AB = p = a + r
We are given the hypotenuse CA = AN + NC
=p + q - 6 = a + b
Or using the values of p and q.
We get
b + r + a + r - 6 = a + b
r=3 cm
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In a right angle triangle ABC with vertex B being the right angle, the mutually perpendicular sides AB and BC are p cm and q cm long respectively. If the length of the hypotenuse is (p + q — 6)cm, the radius of the largest possible circle that can be inscribed in the triangle isa)1.5 cmb)3 cmc)6 cmd)3.3 cmCorrect answer is option 'B'. Can you explain this answer?
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In a right angle triangle ABC with vertex B being the right angle, the mutually perpendicular sides AB and BC are p cm and q cm long respectively. If the length of the hypotenuse is (p + q — 6)cm, the radius of the largest possible circle that can be inscribed in the triangle isa)1.5 cmb)3 cmc)6 cmd)3.3 cmCorrect answer is option 'B'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about In a right angle triangle ABC with vertex B being the right angle, the mutually perpendicular sides AB and BC are p cm and q cm long respectively. If the length of the hypotenuse is (p + q — 6)cm, the radius of the largest possible circle that can be inscribed in the triangle isa)1.5 cmb)3 cmc)6 cmd)3.3 cmCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a right angle triangle ABC with vertex B being the right angle, the mutually perpendicular sides AB and BC are p cm and q cm long respectively. If the length of the hypotenuse is (p + q — 6)cm, the radius of the largest possible circle that can be inscribed in the triangle isa)1.5 cmb)3 cmc)6 cmd)3.3 cmCorrect answer is option 'B'. Can you explain this answer?.
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ample number of questions to practice In a right angle triangle ABC with vertex B being the right angle, the mutually perpendicular sides AB and BC are p cm and q cm long respectively. If the length of the hypotenuse is (p + q — 6)cm, the radius of the largest possible circle that can be inscribed in the triangle isa)1.5 cmb)3 cmc)6 cmd)3.3 cmCorrect answer is option 'B'. Can you explain this answer? tests, examples and also practice Mechanical Engineering tests.
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