Question:
An equilateral triangle of side 9 cm is inscribed in a circle. Find the radius of the circle.
Solution:
Let ABC be an equilateral triangle of side 9 cm and let AD is one of its median.
Let G be the centroid of ΔABC. Then AG: GD = 2 : 1
We know that in an equilateral triangle, centroid coincides with the circum centre.
Therefore, G is the centre of the circumference with circum radius GA.
Also G is the centre and GD is perpendicular to BC.
Therefore, In right triangle ADB, we have
$A B^{2}=A D^{2}+D B^{2}$
$\Rightarrow 9^{2}=\mathrm{AD}^{2}+\mathrm{DB}^{2}$
$\Rightarrow A D=\sqrt{81-\frac{81}{4}}=\frac{9 \sqrt{3}}{2} \mathrm{~cm}$
$\therefore$ Radius $=\mathrm{AG}=\frac{2}{3} \mathrm{AD}=3 \sqrt{3} \mathrm{~cm}$
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All Study Material
- JEE Main
- Exam Pattern
- Previous Year Papers
- PYQ Chapterwise
- Physics
- Kinematics 1D
- Kinemetics 2D
- Friction
- Work, Power, Energy
- Centre of Mass and Collision
- Rotational Dynamics
- Gravitation
- Calorimetry
- Elasticity
- Thermal Expansion
- Heat Transfer
- Kinetic Theory of Gases
- Thermodynamics
- Simple Harmonic Motion
- Wave on String
- Sound waves
- Fluid Mechanics
- Electrostatics
- Current Electricity
- Capacitor
- Magnetism and Matter
- Electromagnetic Induction
- Atomic Structure
- Dual Nature of Matter
- Nuclear Physics
- Radioactivity
- Semiconductors
- Communication System
- Error in Measurement & instruments
- Alternating Current
- Electromagnetic Waves
- Wave Optics
- X-Rays
- All Subjects
- Physics
- Motion in a Plane
- Law of Motion
- Work, Energy and Power
- Systems of Particles and Rotational Motion
- Gravitation
- Mechanical Properties of Solids
- Mechanical Properties of Fluids
- Thermal Properties of matter
- Thermodynamics
- Kinetic Theory
- Oscillations
- Waves
- Electric Charge and Fields
- Electrostatic Potential and Capacitance
- Current Electricity
- Thermoelectric Effects of Electric Current
- Heating Effects of Electric Current
- Moving Charges and Magnetism
- Magnetism and Matter
- Electromagnetic Induction
- Alternating Current
- Electromagnetic Wave
- Ray Optics and Optical Instruments
- Wave Optics
- Dual Nature of Radiation and Matter
- Atoms
- Nuclei
- Semiconductor Electronics: Materials, Devices and Simple Circuits.
- Chemical Effects of Electric Current,
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