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ABC is a right angled triangle, right angled at B such that BC = 6 cm and AB = 8 cm. A circle with centre O is inscribed in ΔABC. The radius of the circle is
- a)1 cm
- b)2 cm
- c)3 cm
- d)4 cm
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
ABC is a right angled triangle, right angled at B such that BC = 6 cm ...
Given that:In right ∆ABC
angle B=90�
BC=6cm
AB=8cm
Let the radius of circle with centre o inscribed in the circle=r cm
By construction in the given image
AB, BC and CA are the tangents to the circle at points P, M and N
By Pythagoras theorem,
CA
2= AB
2+ BC
2⇒ CA
2= 8
2+ 6
2⇒ CA2 = 100
⇒ CA = 10 cm
Area of ∆ABC = Area ∆OAB + Area ∆OBC + Area ∆OCA
24=1/2(r)�AB +1/2(r) �BC+1/2(r) AC
r=2Cm
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ABC is a right angled triangle, right angled at B such that BC = 6 cm ...
The triangle ABC. Let the point of contact of the circle with AB be D.
Since AB is the hypotenuse of the right triangle ABC, we can use the Pythagorean theorem to find the length of AC.
AC^2 = BC^2 + AB^2
AC^2 = 6^2 + 8^2
AC^2 = 36 + 64
AC^2 = 100
AC = 10 cm
Now, let's draw the circle with center O inscribed in triangle ABC. Since the point of contact of the circle with AB is D, we can draw the radius OD perpendicular to AB.
Since the radius OD is perpendicular to AB, triangle ADO is a right triangle.
We know that the length of AC is 10 cm and the length of BC is 6 cm. Therefore, the length of AD is equal to AC - CD.
AD = AC - CD
AD = 10 - 6
AD = 4 cm
Now, we can find the length of BD using the Pythagorean theorem.
BD^2 = AB^2 - AD^2
BD^2 = 8^2 - 4^2
BD^2 = 64 - 16
BD^2 = 48
BD = √48 = 4√3 cm
Therefore, the length of BD is 4√3 cm.
Since AB is the hypotenuse of the right triangle ABC, we can use the Pythagorean theorem to find the length of AC.
AC^2 = BC^2 + AB^2
AC^2 = 6^2 + 8^2
AC^2 = 36 + 64
AC^2 = 100
AC = 10 cm
Now, let's draw the circle with center O inscribed in triangle ABC. Since the point of contact of the circle with AB is D, we can draw the radius OD perpendicular to AB.
Since the radius OD is perpendicular to AB, triangle ADO is a right triangle.
We know that the length of AC is 10 cm and the length of BC is 6 cm. Therefore, the length of AD is equal to AC - CD.
AD = AC - CD
AD = 10 - 6
AD = 4 cm
Now, we can find the length of BD using the Pythagorean theorem.
BD^2 = AB^2 - AD^2
BD^2 = 8^2 - 4^2
BD^2 = 64 - 16
BD^2 = 48
BD = √48 = 4√3 cm
Therefore, the length of BD is 4√3 cm.
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ABC is a right angled triangle, right angled at B such that BC = 6 cm and AB = 8 cm. A circle with centre O is inscribed in ΔABC. The radius of the circle isa)1 cmb)2 cmc)3 cmd)4 cmCorrect answer is option 'B'. Can you explain this answer?
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ABC is a right angled triangle, right angled at B such that BC = 6 cm and AB = 8 cm. A circle with centre O is inscribed in ΔABC. The radius of the circle isa)1 cmb)2 cmc)3 cmd)4 cmCorrect answer is option 'B'. Can you explain this answer? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about ABC is a right angled triangle, right angled at B such that BC = 6 cm and AB = 8 cm. A circle with centre O is inscribed in ΔABC. The radius of the circle isa)1 cmb)2 cmc)3 cmd)4 cmCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for ABC is a right angled triangle, right angled at B such that BC = 6 cm and AB = 8 cm. A circle with centre O is inscribed in ΔABC. The radius of the circle isa)1 cmb)2 cmc)3 cmd)4 cmCorrect answer is option 'B'. Can you explain this answer?.
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ABC is a right angled triangle, right angled at B such that BC = 6 cm and AB = 8 cm. A circle with centre O is inscribed in ΔABC. The radius of the circle isa)1 cmb)2 cmc)3 cmd)4 cmCorrect answer is option 'B'. Can you explain this answer?, a detailed solution for ABC is a right angled triangle, right angled at B such that BC = 6 cm and AB = 8 cm. A circle with centre O is inscribed in ΔABC. The radius of the circle isa)1 cmb)2 cmc)3 cmd)4 cmCorrect answer is option 'B'. Can you explain this answer? has been provided alongside types of ABC is a right angled triangle, right angled at B such that BC = 6 cm and AB = 8 cm. A circle with centre O is inscribed in ΔABC. The radius of the circle isa)1 cmb)2 cmc)3 cmd)4 cmCorrect answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
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