Properties of Triangles · Mathematics · AP EAPCET
MCQ (Single Correct Answer)
$$ \text { In } \triangle A B C, \frac{r_2\left(r_1+r_3\right)}{\sqrt{r_1 r_2+r_2 r_3+r_3 r_1}} \text { is equal to } $$
In $a \triangle A B C$ if $r: R: r_2=1: 3: 7$, then $\sin (A+C)+\sin B$ is equal to
In $\triangle A B C,\left(r_1+r_2\right) \operatorname{cosec}^2 \frac{C}{2}$ is equal to
In a $\triangle A B C$, if $A, B$ and $C$ are in arithmetic progression and $\cos A+\cos B+\cos C=\frac{1+\sqrt{2}+\sqrt{3}}{2 \sqrt{2}}$, then $\tan A$ :
In $\triangle A B C$, if $b+c: c+a: a+b=7: 8: 9$, then the smaller angle (in radians) of that triangle is
| List I | List II | ||
|---|---|---|---|
| (A) | $$ \sum \cot A $$ |
(i) | $$ (a+b+c)^2 \frac{1}{4 \Delta} $$ |
| (B) | $$ \sum \cot \frac{A}{2} $$ |
(ii) | $$ \left(a^2+b^2+c^2\right) \frac{1}{4 \Delta} $$ |
| (C) | If $\tan A: \tan B: \tan C=1: 2: 3$, then $\sin A: \sin B: \sin C=$ | (iii) | $$ 8: 6: 5 $$ |
| (D) | $$ \begin{aligned} &\text { If } \cot \frac{A}{2}: \cot \frac{B}{2}: \cot \frac{C}{2}=3: 7: 9\\ &\text { then } a: b: c= \end{aligned} $$ |
(iv) | $$ 12: 5: 13 $$ |
| (v) | $$ \sqrt{5}: 2 \sqrt{2}: 3 $$ |
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| (vi) | $$ 4 \Delta $$ |
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In any $$\triangle A B C, \frac{\cos A}{a}+\frac{\cos B}{b}+\frac{\cos C}{c}=$$
In a $$\triangle A B C$$, if $$r_1=36, r_2=18$$ and $$r_3=12$$, then $$s=$$
In a $$\triangle A B C, a=6, b=5$$ and $$c=4$$, then $$\cos 2 A=$$
In a $$\triangle A B C,\left(\tan \frac{A}{2} \tan \frac{B}{2} \tan \frac{C}{2}\right)^2 \leq$$
In a $$\triangle A B C, 2(b c \cos A+a c \cos B+a b \cos C)=$$
In a $$\triangle A B C, \frac{a}{b}=2+\sqrt{3}$$ and $$\angle C=60^{\circ}$$. Then, the measure of $$\angle A$$ is
If $$a=2, b=3, c=4$$ in a $$\triangle A B C$$, then $$\cos C=$$
In a $$\triangle A B C$$ $$(b+c) \cos A+(c+a) \cos B+(a+b) \cos C=$$
Suppose $$\triangle A B C$$ is an isosceles triangle with $$\angle C=90^{\circ}, A=(2,3)$$ and $$B=(4,5)$$. Then, the centroid of the triangle is
In a $$\triangle A B C$$, if $$a \neq b, \frac{a \cos A-b \cos B}{a \cos B-b \cos A}+\cos C=$$
If in a $$\triangle A B C, a=2, b=3$$ and $$c=4$$, then $$\tan (A / 2)=$$
If the angles of a $$\triangle A B C$$ are in the ratio $$1: 2: 3$$, then the corresponding sides are in the ratio
In a $$\triangle A B C, r_1 \cot \frac{A}{2}+r_2 \cot \frac{B}{2}+r_3 \cot \frac{C}{2}=$$
In $$\triangle A B C$$, medians $$A D$$ and $$B E$$ are drawn. If $$A D=4, \angle D A B=\frac{\pi}{6}$$ and $$\angle A B E=\frac{\pi}{3}$$, then the area of $$\triangle A B C$$ is
In a $$\triangle A B C, 2 \Delta^2=\frac{a^2 b^2 c^2}{a^2+b^2+c^2}$$, then the triangle is
In $$\triangle A B C$$, suppose the radius of the circle opposite to an angle $$A$$ is denoted by $$r_1$$, similarly $$r_2 \leftrightarrow$$ angle $$B, r_3 \leftrightarrow$$ angle $$C$$. If $$r_1=2, r_2=3, r_3=6$$, what is the value of $$r_1+r_2+r_3-r=$$ (R - radius of the circum circle).
In a $$\Delta ABC$$, if a = 3, b = 4 and $$\sin A=\frac{3}{4}$$, then $$\angle CBA$$ is equal to
In $$\Delta ABC,A=75\Upsilon$$ and $$B=45\Upsilon$$, then the value of $$b+c\sqrt2$$ is equal to
In $$\triangle A B C$$, suppose the radius of the circle opposite to an $$\angle A$$ is denoted by $$r_1$$, similarly $$r_2 \leftrightarrow \angle B$$ and $$r_3 \leftrightarrow \angle C$$. If $$r$$ is the radius of inscribed circle, then, what is the value of $$\frac{a b-r_1 r_2}{r_3}$$ is equal to
If D, E and F are respectively mid-points of AB, AC and BC in $$\Delta ABC$$, then BE + AF is equal to