MCQ
In an isosceles triangle $ABC ,$ if $AC = BC$ and $AB ^2=2 AC ^2$ then $\angle C =$ ?
- A$30^{\circ}$
- B$45^{\circ}$
- C$60^{\circ}$
- ✓$90^{\circ}$
✓
Answer
Correct option: D.
$90^{\circ}$
Given, $AB ^2=2 AC ^2$
$\Rightarrow AB^2=AC^2+AC^2 .$
$\Rightarrow AB^2=AC^2+BC^2 .(\because AC=BC)$
$\therefore$ By the converse of Pythagoras theorem, we have $\angle C =90^{\circ}$.
$\Rightarrow AB^2=AC^2+AC^2 .$
$\Rightarrow AB^2=AC^2+BC^2 .(\because AC=BC)$
$\therefore$ By the converse of Pythagoras theorem, we have $\angle C =90^{\circ}$.
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
The product of the zeros of $x^3+4 x^2+x-6$ is
→→
The $\text{HCF}$ of $256,442$ and $940$ is :
→If $\tan A=\sqrt{2}-1$, then what is the value of $\frac{\tan A}{1+\tan ^2 A}$ ?
→Which of the following cennot be the probability of an event?
A steel wire when bent in the form of a square enclosed an area of $121 cm ^2$. If the same wire is bent in the form of a circle, then the circumference of the circle is
→Value of $\tan 30^{\circ} \operatorname{cosec} 60^{\circ}+\tan 60^{\circ} \sec 30^{\circ}=?$
→In the given figure $,RQ$ is a tangent to the circle with centre $O$. If $SQ = 6\ cm$ and $QR = 4\ cm,$ then $OR$ is equal to :
→A number is selected from first 50 natural numbers. What is the probability that it is a multiple of 3 or 5?
The tops of two poles of height $18 m$ and $10 m$ are connected by a wire of length $l$. If the wire makes an angle of $30^{\circ}$ with the horizontal, then $l$ is equal to
→