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5. AB is a diameter of a circle and C is any point on the circumference of the circle. Then

(a) The area of DABC is maximum when it is isosceles

(b) The area of DABC is minimum when it is isosceles

(c) The perimeter of DABC if maximum when it is isosceles

(d) None of these

Simran Bhatia , 11 Years ago
Grade 11
anser 1 Answers
Jitender Singh

Last Activity: 11 Years ago

Ans: (a)
Sol:
Let the circle be
x^{2}+y^{2}=(\frac{AB}{2})^{2}
Let AB is the the diameter on the x-axis. Then coordinates of C will be:
(\frac{AB}{2}cos\theta , \frac{AB}{2}sin\theta )
Then area A of triangle ABC will be
A = \frac{1}{2}.AB.\frac{ABsin\theta }{2}
A = \frac{AB^{2}}{4}sin\theta
A is maximum when sin value is maximum which is 1.
sin\theta =1
cos\theta =0
Then coordinates of C will be:
(0, \frac{AB}{2})
which proves that ABC is an isosceles triangle.
Thanks & Regards
Jitender Singh
IIT Delhi
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