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Question Number 63206 by lalitchand last updated on 30/Jun/19

Commented by lalitchand last updated on 30/Jun/19

$$\mathrm{question}\mathrm{number}8$$

Answered by arcana last updated on 01/Jul/19

$$\mathrm{sea}\mathrm{E}\mathrm{el}\mathrm{punto}\mathrm{de}\mathrm{interseccion}\mathrm{entre}$$$$\mathrm{los}\mathrm{segmentos}\mathrm{DB}\mathrm{y}\mathrm{AC}\mathrm{tal}\mathrm{que}$$$$\stackrel{\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}}{\mathrm{DE}}+\stackrel{\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}}{\mathrm{EB}}=\stackrel{\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}}{\mathrm{DB}};\stackrel{\mathrm{\_}\mathrm{\_}\mathrm{\_}}{\mathrm{AE}}+\stackrel{\mathrm{\_}\mathrm{\_}\mathrm{\_}}{\mathrm{EC}}=\stackrel{\mathrm{\_}\mathrm{\_}\mathrm{\_}}{\mathrm{AC}}$$$$$$$$\mathrm{por}\mathrm{hipotesis}m\mathrm{\angle }\mathrm{BDC}=m\mathrm{\angle }\mathrm{ACD}$$$$\mathrm{luego}\mathrm{el}\mathrm{triangulo}△\mathrm{DEC}\mathrm{es}\mathrm{isosceles}$$$$\Rightarrow \stackrel{\mathrm{\_}\mathrm{\_}\mathrm{\_}}{\mathrm{DE}}=\stackrel{\mathrm{\_}\mathrm{\_}\mathrm{\_}}{\mathrm{EC}}\left(1\right)$$$$\mathrm{por}\mathrm{otro}\mathrm{lado},m\mathrm{\angle }\mathrm{ACB}=m\mathrm{\angle }\mathrm{ADB}\left(2\right)$$$$\mathrm{y}\mathrm{como}\mathrm{los}\mathrm{angulos}\mathrm{\angle }\mathrm{DEA},\mathrm{\angle }\mathrm{CEB}$$$$\mathrm{son}\mathrm{opuestos}\mathrm{por}\mathrm{el}\mathrm{vertice}\mathrm{E}\mathrm{entonces}$$$$\mathrm{\angle }\mathrm{DEA}\cong \mathrm{\angle }\mathrm{CEB}\Rightarrow m\mathrm{\angle }\mathrm{DEA}=m\mathrm{\angle }\mathrm{CEB}\left(3\right)$$$$$$$$\mathrm{por}\left(1\right),\left(2\right)\mathrm{y}\left(3\right),△\mathrm{ADE}=△\mathrm{BCE}\left(\mathrm{ALA}\right)$$$$\Rightarrow \stackrel{\mathrm{\_}\mathrm{\_}\mathrm{\_}}{\mathrm{AE}}=\stackrel{\mathrm{\_}\mathrm{\_}\mathrm{\_}}{\mathrm{EB}}$$$$\Rightarrow \mathrm{DB}=\mathrm{DE}+\mathrm{EB}=\mathrm{AE}+\mathrm{EC}=\mathrm{AC}$$$$$$

Commented by lalitchand last updated on 01/Jul/19

$$\mathrm{Question}\mathrm{nmbr}8\mathrm{not}7$$

Commented by arcana last updated on 01/Jul/19

$$\mathrm{its}\mathrm{the}\mathrm{answer}\mathrm{question}8$$

Commented by arcana last updated on 01/Jul/19

Commented by lalitchand last updated on 01/Jul/19

$$\mathrm{thanks}\mathrm{you}\mathrm{i}\mathrm{understand}$$

Commented by lalitchand last updated on 01/Jul/19

$$\mathrm{Can}\mathrm{you}\mathrm{solve}10\mathrm{number}..\mathrm{i}\mathrm{have}\mathrm{recently}$$$$\mathrm{posted}$$

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