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Question Number 186998 by Mingma last updated on 12/Feb/23

Commented by a.lgnaoui last updated on 12/Feb/23

Answered by a.lgnaoui last updated on 12/Feb/23

$$△ABC$$$$\frac{\sin 12}{X}=\frac{\sin 18}{AD}\left(1\right)$$$$△ABC$$$$12+18+48+\measuredangle CAD=180$$$$\Rightarrow \measuredangle CAD=102\Rightarrow \measuredangle ADC=180-150=30$$$$△ADC\frac{\sin 48}{AD}=\frac{\sin 30}{Y}\left(2\right)$$$$\left(1\right)\Rightarrow X\sin 18=AD\sin 12$$$$\left(2\right)\Rightarrow Y\sin 48=AD\sin 30$$$$\frac{\left(1\right)}{\left(2\right)}\Rightarrow \frac{X\sin 18}{Y\sin 48}=\frac{\sin 12}{\sin 30}$$$$\frac{X}{Y}=\frac{\sin 12\times \sin 48}{\sin 30\times \sin 18}=1$$$$$$$$doncX=Y$$$$$$

Commented by Rupesh123 last updated on 13/Feb/23

Good

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