In ABC, if a, b, c are in A.P. (with usual notations), identify t… - Vidyadip

MCQ

In $\Delta ABC$, if $a, b, c$ are in $A.P.$ (with usual notations), identify the incorrect statements -

A
$h_1, h_2, h_3$ are in $H.P.$, where $h_1, h_2, h_3$ are altitudes from vertices $A,B$ $C$ respectively.
B
$sinA, sinB, sinC$ are in $A.P.$
✓
$r_1, r_2, r_3$ are in $A.P.$
D
$tan \frac{A}{2} , tan \frac{B}{2}, tan \frac{C}{2} $ are in $H.P.$

✓

Answer

Correct option: C.

$r_1, r_2, r_3$ are in $A.P.$

c
$\mathrm{a}, \mathrm{b}, \mathrm{c}$ are in $\mathrm{AP}.$

$\lambda \mathrm{a}, \lambda \mathrm{b}, \lambda \mathrm{c}$ will be in $\mathrm{AP}.$

$\Rightarrow \sin A, \sin B, \sin C$ in $A P.$

Also $\mathrm{h}_{1}=\frac{2 \Delta}{\mathrm{a}} ; \mathrm{h}_{2}=\frac{2 \Delta}{\mathrm{b}} ; \mathrm{h}_{3}=\frac{2 \Delta}{\mathrm{c}}$ will be in $HP.$

$a, b, c$ in $A P \Rightarrow s-a, s-b, s-c$ in $A P$

$\Rightarrow \frac{\Delta}{s-a}, \frac{\Delta}{s-b} ; \frac{\Delta}{s-c}$ will be in $HP.$

$\Rightarrow \mathrm{r}_{1}, \mathrm{r}_{2}, \mathrm{r}_{3}$ in $H.P.$

Also $\frac{\Delta}{s(s-a)}, \frac{\Delta}{s(s-b)}, \frac{\Delta}{s(s-c)}$ will be in $HP.$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "M.C.Q (1 Marks)" from STD 11 - 8. sequence and series→STD 11 - 8. sequence and series — all question types→Maths STD 11 Science question papers→CBSE Board STD 11 Science question papers→CBSE Board question paper generator→

Similar questions

Let the tangent to the curve $x^2+2 x-4 y+9=0$ at the point $P (1,3)$ on it meet the $y$-axis at $A$. Let the line passing through $P$ and parallel to the line $x -$ $3 y=6$ meet the parabola $y^2=4 x$ at $B$. If $B$ lies on the line $2 x-3 y=8$. then $(A B)^2$ is equal to $............$.

The lines $15x - 18y + 1 = 0,$ $12x + 10y - 3 = 0$ and $6x + 66y - 11 = 0$ are

The number of values of $x$ in the interval $[0, 5 \pi ] $ satisfying the equation $3{\sin ^2}x - 7\sin x + 2 = 0$ is

The coefficient of $x^{-5}$ in the binomial expansion of ${\left( {\frac{{x + 1}}{{{x^{\frac{2}{3}}} - {x^{\frac{1}{3}}} + 1}} - \frac{{x - 1}}{{x - {x^{\frac{1}{2}}}}}} \right)^{10}}$ where $x \ne 0, 1$ , is

The line $(3x - y + 5) + \lambda (2x - 3y - 4) = 0$ will be parallel to $y$-axis, if $\lambda$ =

The set of values of $'a'$ such that $x^2 -2ax + a^2 -6a \leqslant 0$ in $[1, 2]$ is

The period of the function $\text{f(x)}=\sin \big(\frac{2\pi\text{x}}{3}\big)+\cos\big(\frac{\pi\text{x}}{3}\big)$:

In the Argand plane, the vector $z = 4 - 3i$ is turned in the clockwise sense through ${180^o}$and stretched three times. The complex number represented by the new vector is

The vertices of a triangle are $\mathrm{A}(-1,3), \mathrm{B}(-2,2)$ and $\mathrm{C}(3,-1)$. $A$ new triangle is formed by shifting the sides of the triangle by one unit inwards. Then the equation of the side of the new triangle nearest to origin is :

If the mean and variance of the data $65,68,58,44$, $48,45,60, \alpha, \beta, 60$ where $\alpha>\beta$ are $56$ and $66.2$ respectively, then $\alpha^2+\beta^2$ is equal to