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As shown is figure, points A and C are on a circle. A − O − B where O is center of circle.
AB = 10, BC = 5 and AB ⊥ BC.
Find Radius of the circle.?
AB = 10, BC = 5 and AB ⊥ BC.
Find Radius of the circle.?
Most Upvoted Answer
As shown is figure, points A and C are on a circle. A − O − B where O ...
Understanding the Problem
To find the radius of the circle given the points A, B, C, and the dimensions provided, we will visualize the setup.
- Point O is the center of the circle.
- AB = 10 and BC = 5, with AB being perpendicular to BC.
Visualizing the Geometry
- Draw the right triangle formed by points A, B, and C.
- Since AB is perpendicular to BC, we can apply the Pythagorean theorem.
Calculating AC
- Using Pythagorean theorem:
AC = √(AB² + BC²)
AC = √(10² + 5²)
AC = √(100 + 25)
AC = √125
AC = 5√5
Finding the Radius
- Since points A and C lie on the circle, the distance from the center O to points A and C will be equal to the radius (r).
- The radius can be calculated as follows:
- The radius O to A can be expressed in terms of OA and AB as:
OA = √(OB² + AB²)
Here, OB is the radius (r), and AB = 10.
- Since OA is a radius, we have:
OA = r,
Thus, r = √(r² + 10²).
Final Radius Calculation
- From the triangle OAB:
r² = (5√5)² + (10)²
r² = 125 + 100
r² = 225
r = √225 = 15.
Conclusion
- The radius of the circle is 15 units. This completes our calculation based on the given triangle and circle properties.
To find the radius of the circle given the points A, B, C, and the dimensions provided, we will visualize the setup.
- Point O is the center of the circle.
- AB = 10 and BC = 5, with AB being perpendicular to BC.
Visualizing the Geometry
- Draw the right triangle formed by points A, B, and C.
- Since AB is perpendicular to BC, we can apply the Pythagorean theorem.
Calculating AC
- Using Pythagorean theorem:
AC = √(AB² + BC²)
AC = √(10² + 5²)
AC = √(100 + 25)
AC = √125
AC = 5√5
Finding the Radius
- Since points A and C lie on the circle, the distance from the center O to points A and C will be equal to the radius (r).
- The radius can be calculated as follows:
- The radius O to A can be expressed in terms of OA and AB as:
OA = √(OB² + AB²)
Here, OB is the radius (r), and AB = 10.
- Since OA is a radius, we have:
OA = r,
Thus, r = √(r² + 10²).
Final Radius Calculation
- From the triangle OAB:
r² = (5√5)² + (10)²
r² = 125 + 100
r² = 225
r = √225 = 15.
Conclusion
- The radius of the circle is 15 units. This completes our calculation based on the given triangle and circle properties.
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As shown is figure, points A and C are on a circle. A − O − B where O is center of circle. AB = 10, BC = 5 and AB ⊥ BC. Find Radius of the circle.?
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As shown is figure, points A and C are on a circle. A − O − B where O is center of circle. AB = 10, BC = 5 and AB ⊥ BC. Find Radius of the circle.? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about As shown is figure, points A and C are on a circle. A − O − B where O is center of circle. AB = 10, BC = 5 and AB ⊥ BC. Find Radius of the circle.? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for As shown is figure, points A and C are on a circle. A − O − B where O is center of circle. AB = 10, BC = 5 and AB ⊥ BC. Find Radius of the circle.?.
As shown is figure, points A and C are on a circle. A − O − B where O is center of circle. AB = 10, BC = 5 and AB ⊥ BC. Find Radius of the circle.? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about As shown is figure, points A and C are on a circle. A − O − B where O is center of circle. AB = 10, BC = 5 and AB ⊥ BC. Find Radius of the circle.? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for As shown is figure, points A and C are on a circle. A − O − B where O is center of circle. AB = 10, BC = 5 and AB ⊥ BC. Find Radius of the circle.?.
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