Circle 1 Question 10
10. $A B$ is a diameter of a circle and $C$ is any point on the circumference of the circle. Then,
(1983, 1M)
(a) the area of $\triangle A B C$ is maximum when it is isosceles
(b) the area of $\triangle A B C$ is minimum when it is isosceles
(c) the perimeter of $\triangle A B C$ is minimum when it is isosceles
(d) None of the above
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Answer:
Correct Answer: 10. (b, c)
Solution:
- Clearly, $\angle C=90^{\circ}$ as angle in semi-circle is right angled. Now, area of triangle is maximum when $A C=B C$. i.e. Triangle is right angled isosceles.
