MCQ
In an isosceles triangle $ABC$ if $AC = BC$ and $AB^2 = 2AC^2$, then $\angle\text{C}=$
- A$30^\circ$
- B$45^\circ$
- ✓$90^\circ$
- D$60^\circ$
✓
Answer
Correct option: C.
$90^\circ$
In isosceles $\triangle\text{ABC},\ \text{AC}=\text{BC}$
and $AB^2 = AC^2 + AC^2 = 2AC^2$
$= AC^2 + BC^2 (AC = BC)$
By converse of Pythagoras Theorem,
$\angle\text{C}=90^\circ$
and $AB^2 = AC^2 + AC^2 = 2AC^2$
$= AC^2 + BC^2 (AC = BC)$
By converse of Pythagoras Theorem,
$\angle\text{C}=90^\circ$
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
Median $=?$
→If $A(2, 2), B(-4, -4)$ and $C(5, -8)$ are the vertices of a triangle, then the length of the median through vertices $C$ is:
→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:
→$\frac{1+\cot ^2 A }{1+\tan ^2 A }=?$
→A bag contains $3$ white, $4$ red and $5$ black balls. One ball is drawn at random. What is the probability that the ball drawn is neither black nor white?
→In a circle of radius $14\ cm$. an arc subtends an angle of $120^\circ $ at the centre. If $\sqrt{3}=1.73$ then the area of the segment of the circle is:
→In the given figure, $O$ is the centre of the circle. $\text{AB}$ is the tangent to the circle at the point $P$. If $\angle\text{APQ}=58^\circ$ then the measure of $\angle\text{PQB}$ is:
→Mark the correct alternative in the following:
The common difference of an $A.P.$, the sum of whose n terms is $S_n$, is
→The common difference of an $A.P.$, the sum of whose n terms is $S_n$, is
The height of a conical tent is $14\ m$ and its floor area is $346.5m^2$. How much canvas, $1.1$ wide, will be required for it?
→What is the probability of an impossible event?