JEE Exam > JEE Questions > LET ABCD be a quadrilateral with area 18 ,wit...
Start Learning for Free
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?
Verified Answer
LET ABCD be a quadrilateral with area 18 ,with side AB parallel to the...
This question is part of UPSC exam. View all JEE courses
Most Upvoted Answer
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
Attention JEE Students!
To make sure you are not studying endlessly, EduRev has designed JEE study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in JEE.
|
|
Explore Courses for JEE exam
|
|
Similar JEE Doubts
Top Courses for JEEView all
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?
Question Description
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.
Download more important topics, notes, lectures and mock test series for JEE Exam by signing up for free.
Here you can find the meaning 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? defined & explained in the simplest way possible. Besides giving the explanation 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?, 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
ample number of questions to practice 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? tests, examples and also practice JEE tests.
|
|
Explore Courses for JEE exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup