Question:
In an isosceles triangle $\mathrm{ABC}$ if $\mathrm{AC}=\mathrm{BC}$ and $\mathrm{AB}^{2}=2 \mathrm{AC}^{2}$, then $\angle \mathrm{C}=$
(a) $30^{\circ}$
(b) $45^{\circ}$
(C) $90^{\circ}$
(d) $60^{\circ}$
Solution:
Given: In Isosceles $\triangle \mathrm{ABC}, \mathrm{AC}=\mathrm{BC}$ and $\mathrm{AB}^{2}=2 \mathrm{AC}^{2}$.
To find: Measure of angle C
In Isosceles ΔABC,
AC = BC
∠B=∠A (Equal sides have equal angles opposite to them)
$\mathrm{AB}^{2}=2 \mathrm{AC}^{2}$
$\mathrm{AB}^{2}=\mathrm{AC}^{2}+\mathrm{AC}^{2}$
$\mathrm{AB}^{2}=\mathrm{AC}^{2}+\mathrm{BC}^{2}(\mathrm{AC}=\mathrm{BC})$
$\Rightarrow \triangle \mathrm{ABC}$ is right angle triangle, with $\angle \mathrm{C}=90^{\circ}$
Hence the correct answer is $(c)$.
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- 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
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- Atoms
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