A) \[r\cos ec\alpha \sin \frac{\beta }{2}\]
B) \[r\sin \alpha \cos ec\frac{\beta }{2}\]
C) \[r\sin \frac{\alpha }{2}\cos ec\beta \]
D) \[r\cos ec\frac{\alpha }{2}\sin \beta \]
Correct Answer: D
Solution :
In\[\Delta \,\,APC\],\[\sin (\angle PAC)=\frac{CP}{AC}\] \[\Rightarrow \]\[AC=\frac{r}{\sin \frac{\alpha }{2}}=r\,\,\cos ec\frac{\alpha }{2}\] ... (i) Again in\[\Delta ABC\], \[\sin \beta =\frac{BC}{AC}\] \[\Rightarrow \] \[BC=AC\,\,\sin \beta \] \[\Rightarrow \] \[H=r\sin \beta \cos ec\left( \frac{\alpha }{2} \right)\] [from Eq, (i)]You need to login to perform this action.
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