Class 11MathematicsTrigonometrical EquationsMix Examples-Trigonometrical Equations and Inequations, Properties of Triangles, Height and Distance
DifficultIn a $\triangle ABC$,with usual notation,match the items in List-$I$ with the items in List-$II$ and choose the correct option.
List-$I$ List-$II$ $(A) \ r_1 r_2 \sqrt{\frac{4R-r_1-r_2}{r_1+r_2}}$ $1. \ b$ $(B) \ \frac{r_2(r_3+r_1)}{\sqrt{r_1r_2+r_2r_3+r_3r_1}}$ $2. \ a^2, b^2, c^2 \text{ are in } AP$ $(C) \ \frac{a}{c} = \frac{\sin(A-B)}{\sin(B-C)}$ $3. \ \Delta$ $(D) \ bc \cos^2 \frac{A}{2}$ $4. \ R r_1 r_2 r_3$ $5. \ s(s-a)$
| List-$I$ | List-$II$ |
| $(A) \ r_1 r_2 \sqrt{\frac{4R-r_1-r_2}{r_1+r_2}}$ | $1. \ b$ |
| $(B) \ \frac{r_2(r_3+r_1)}{\sqrt{r_1r_2+r_2r_3+r_3r_1}}$ | $2. \ a^2, b^2, c^2 \text{ are in } AP$ |
| $(C) \ \frac{a}{c} = \frac{\sin(A-B)}{\sin(B-C)}$ | $3. \ \Delta$ |
| $(D) \ bc \cos^2 \frac{A}{2}$ | $4. \ R r_1 r_2 r_3$ |
| $5. \ s(s-a)$ |
- A$A-4, B-3, C-1, D-5$
- B$A-5, B-4, C-3, D-2$
- C$A-3, B-1, C-2, D-5$
- D$A-4, B-5, C-2, D-1$
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DifficultTS EAMCET 2020
View SolutionWith usual notations in $\triangle ABC$,if $\angle B = \frac{\pi}{2}$,and $\tan \frac{A}{2}, \tan \frac{C}{2}$ are roots of the equation $px^2 + qx + r = 0$,$p \neq 0$,then:
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