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Triangle ABC is drawn to circumscribe a circle radius 2 cm such that segments BD and into which BC is divided by point of contact D are the lengths 4 cm and 3 cm respectively. if area of triangle ABC is 21 cm² then the AB and AC ?
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Triangle ABC is drawn to circumscribe a circle radius 2 cm such that s...
Solution:
Introduction:
Let ABC be a triangle with incenter I, and let the incircle of ABC touch sides BC, CA, and AB at D, E, and F, respectively. Let EF meet BC at X and let DI meet EF at Y. Using properties of tangents to circles, it can be shown that BY = YX = XC.
Given:
Radius of the circle = 2 cm
Length of BD = 4 cm
Length of CD = 3 cm
Area of triangle ABC = 21 cm²
To find:
AB and AC
Solution:
Step 1: Find the perimeter of the triangle ABC
Let s be the semi-perimeter of triangle ABC. The perimeter of triangle ABC is given by:
P = 2s
Step 2: Find the area of triangle ABC
The area of triangle ABC can be found using the formula:
A = sr
where r is the radius of the inscribed circle.
Step 3: Find the inradius of the triangle
The radius of the inscribed circle of triangle ABC is given by:
r = A/s
Step 4: Find the length of AD
The length of AD can be found using the formula:
AD = s - a
Step 5: Find the length of BD and CD
The length of BD and CD can be found using the formula:
BD = s - c
CD = s - b
Step 6: Find the lengths of AB and AC
The lengths of AB and AC can be found using the Pythagorean theorem:
AB² = (s - b)² + r²
AC² = (s - c)² + r²
Step 7: Substitute the given values and solve for AB and AC
Substituting the given values, we get:
s = (4 + 3 + AB + AC)/2 = (7 + AB + AC)/2
A = sr = (s(4+3+AB+AC))/2 = (7s+AB+AC)/2
r = A/s = (7s+AB+AC)/2s
AD = s - a = (7 + AB + AC)/2 - 4 = (1 + AB + AC)/2
BD = s - c = (7 + AB + AC)/2 - 3 = (4 + AB + AC
Community Answer
Triangle ABC is drawn to circumscribe a circle radius 2 cm such that s...
7.5 and 6.5???
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Triangle ABC is drawn to circumscribe a circle radius 2 cm such that segments BD and into which BC is divided by point of contact D are the lengths 4 cm and 3 cm respectively. if area of triangle ABC is 21 cm² then the AB and AC ?
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Triangle ABC is drawn to circumscribe a circle radius 2 cm such that segments BD and into which BC is divided by point of contact D are the lengths 4 cm and 3 cm respectively. if area of triangle ABC is 21 cm² then the AB and AC ? 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 Triangle ABC is drawn to circumscribe a circle radius 2 cm such that segments BD and into which BC is divided by point of contact D are the lengths 4 cm and 3 cm respectively. if area of triangle ABC is 21 cm² then the AB and AC ? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Triangle ABC is drawn to circumscribe a circle radius 2 cm such that segments BD and into which BC is divided by point of contact D are the lengths 4 cm and 3 cm respectively. if area of triangle ABC is 21 cm² then the AB and AC ?.
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