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LET ABCD be a quadrilateral with area 18 ,with side AB parallel to the side CD and AB=2CD .Let AD be perpendicular to AB and CD .If a circle is drawn inside the quadrilateral ABCD touching all the side ,then it's radius is A 3 B 2 C 3/2 D 1?
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LET ABCD be a quadrilateral with area 18 ,with side AB parallel to the...
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LET ABCD be a quadrilateral with area 18 ,with side AB parallel to the...
Given:
- Quadrilateral ABCD with area 18
- Side AB parallel to side CD
- AB = 2CD
- AD is perpendicular to AB and CD
To find: The radius of the circle inscribed in quadrilateral ABCD
Solution:
Step 1: Understanding the Problem
- We are given a quadrilateral ABCD with specific properties.
- We need to find the radius of the circle inscribed in ABCD.
Step 2: Analyzing the Given Information
- We know that the area of a quadrilateral is given by the formula: Area = 1/2 * product of diagonals * sin(angle between diagonals).
- In this case, the diagonals are AD and BC.
- Since AD is perpendicular to AB and CD, AD is also the height of ABCD.
- Let the length of AD be h.
- The area of ABCD is given as 18.
Step 3: Finding the Length of AD
- The area of ABCD is given by: 18 = 1/2 * AD * CD.
- Since AB = 2CD, we can substitute CD with AB/2 in the area formula.
- 18 = 1/2 * AD * (AB/2).
- Simplifying, we get AD = 8.
Step 4: Determining the Length of CD
- Since AB = 2CD, we can substitute AB with 2CD in the area formula.
- 18 = 1/2 * CD * (2CD).
- Simplifying, we get CD^2 = 9.
- Taking the square root of both sides, we get CD = 3.
Step 5: Finding the Length of AB
- Since AB = 2CD, we can substitute CD with 3 in the equation.
- AB = 2 * 3 = 6.
Step 6: Finding the Radius of the Inscribed Circle
- In a quadrilateral, the radius of the inscribed circle is given by the formula: r = 2 * Area / (sum of opposite sides).
- In this case, the opposite sides are AB and CD.
- r = 2 * 18 / (6 + 3).
- Simplifying, we get r = 4.
Step 7: Final Answer
- The radius of the inscribed circle in quadrilateral ABCD is 4. Therefore, the correct option is D) 1.
- Quadrilateral ABCD with area 18
- Side AB parallel to side CD
- AB = 2CD
- AD is perpendicular to AB and CD
To find: The radius of the circle inscribed in quadrilateral ABCD
Solution:
Step 1: Understanding the Problem
- We are given a quadrilateral ABCD with specific properties.
- We need to find the radius of the circle inscribed in ABCD.
Step 2: Analyzing the Given Information
- We know that the area of a quadrilateral is given by the formula: Area = 1/2 * product of diagonals * sin(angle between diagonals).
- In this case, the diagonals are AD and BC.
- Since AD is perpendicular to AB and CD, AD is also the height of ABCD.
- Let the length of AD be h.
- The area of ABCD is given as 18.
Step 3: Finding the Length of AD
- The area of ABCD is given by: 18 = 1/2 * AD * CD.
- Since AB = 2CD, we can substitute CD with AB/2 in the area formula.
- 18 = 1/2 * AD * (AB/2).
- Simplifying, we get AD = 8.
Step 4: Determining the Length of CD
- Since AB = 2CD, we can substitute AB with 2CD in the area formula.
- 18 = 1/2 * CD * (2CD).
- Simplifying, we get CD^2 = 9.
- Taking the square root of both sides, we get CD = 3.
Step 5: Finding the Length of AB
- Since AB = 2CD, we can substitute CD with 3 in the equation.
- AB = 2 * 3 = 6.
Step 6: Finding the Radius of the Inscribed Circle
- In a quadrilateral, the radius of the inscribed circle is given by the formula: r = 2 * Area / (sum of opposite sides).
- In this case, the opposite sides are AB and CD.
- r = 2 * 18 / (6 + 3).
- Simplifying, we get r = 4.
Step 7: Final Answer
- The radius of the inscribed circle in quadrilateral ABCD is 4. Therefore, the correct option is D) 1.
Community Answer
LET ABCD be a quadrilateral with area 18 ,with side AB parallel to the...
B is the correct option
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LET ABCD be a quadrilateral with area 18 ,with side AB parallel to the side CD and AB=2CD .Let AD be perpendicular to AB and CD .If a circle is drawn inside the quadrilateral ABCD touching all the side ,then it's radius is A 3 B 2 C 3/2 D 1?
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LET ABCD be a quadrilateral with area 18 ,with side AB parallel to the side CD and AB=2CD .Let AD be perpendicular to AB and CD .If a circle is drawn inside the quadrilateral ABCD touching all the side ,then it's radius is A 3 B 2 C 3/2 D 1? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about LET ABCD be a quadrilateral with area 18 ,with side AB parallel to the side CD and AB=2CD .Let AD be perpendicular to AB and CD .If a circle is drawn inside the quadrilateral ABCD touching all the side ,then it's radius is A 3 B 2 C 3/2 D 1? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for LET ABCD be a quadrilateral with area 18 ,with side AB parallel to the side CD and AB=2CD .Let AD be perpendicular to AB and CD .If a circle is drawn inside the quadrilateral ABCD touching all the side ,then it's radius is A 3 B 2 C 3/2 D 1?.
LET ABCD be a quadrilateral with area 18 ,with side AB parallel to the side CD and AB=2CD .Let AD be perpendicular to AB and CD .If a circle is drawn inside the quadrilateral ABCD touching all the side ,then it's radius is A 3 B 2 C 3/2 D 1? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about LET ABCD be a quadrilateral with area 18 ,with side AB parallel to the side CD and AB=2CD .Let AD be perpendicular to AB and CD .If a circle is drawn inside the quadrilateral ABCD touching all the side ,then it's radius is A 3 B 2 C 3/2 D 1? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for LET ABCD be a quadrilateral with area 18 ,with side AB parallel to the side CD and AB=2CD .Let AD be perpendicular to AB and CD .If a circle is drawn inside the quadrilateral ABCD touching all the side ,then it's radius is A 3 B 2 C 3/2 D 1?.
Solutions for LET ABCD be a quadrilateral with area 18 ,with side AB parallel to the side CD and AB=2CD .Let AD be perpendicular to AB and CD .If a circle is drawn inside the quadrilateral ABCD touching all the side ,then it's radius is A 3 B 2 C 3/2 D 1? in English & in Hindi are available as part of our courses for JEE.
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LET ABCD be a quadrilateral with area 18 ,with side AB parallel to the side CD and AB=2CD .Let AD be perpendicular to AB and CD .If a circle is drawn inside the quadrilateral ABCD touching all the side ,then it's radius is A 3 B 2 C 3/2 D 1?, a detailed solution for LET ABCD be a quadrilateral with area 18 ,with side AB parallel to the side CD and AB=2CD .Let AD be perpendicular to AB and CD .If a circle is drawn inside the quadrilateral ABCD touching all the side ,then it's radius is A 3 B 2 C 3/2 D 1? has been provided alongside types of LET ABCD be a quadrilateral with area 18 ,with side AB parallel to the side CD and AB=2CD .Let AD be perpendicular to AB and CD .If a circle is drawn inside the quadrilateral ABCD touching all the side ,then it's radius is A 3 B 2 C 3/2 D 1? theory, EduRev gives you an
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