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Question Number 44103 by Raj Singh last updated on 21/Sep/18

Commented by Raj Singh last updated on 21/Sep/18

in this figure PQ∣∣BA and PR∣∣CA  if PD=12 find BD×CD

$${in}\:{this}\:{figure}\:{PQ}\mid\mid{BA}\:{and}\:{PR}\mid\mid{CA} \\ $$$${if}\:{PD}=\mathrm{12}\:{find}\:{BD}×{CD} \\ $$

Answered by MrW3 last updated on 21/Sep/18

ΔDBR∼ΔDPQ  ((BD)/(PD))=((BR)/(PQ))  ΔDPR∼ΔDCQ  ((PD)/(CD))=((PR)/(CQ))  ΔBPR∼ΔPCQ  ((BR)/(PQ))=((PR)/(CQ))  ⇒((BD)/(PD))=((PD)/(CD))  ⇒BD×CD=PD^2 =12^2 =144

$$\Delta{DBR}\sim\Delta{DPQ} \\ $$$$\frac{{BD}}{{PD}}=\frac{{BR}}{{PQ}} \\ $$$$\Delta{DPR}\sim\Delta{DCQ} \\ $$$$\frac{{PD}}{{CD}}=\frac{{PR}}{{CQ}} \\ $$$$\Delta{BPR}\sim\Delta{PCQ} \\ $$$$\frac{{BR}}{{PQ}}=\frac{{PR}}{{CQ}} \\ $$$$\Rightarrow\frac{{BD}}{{PD}}=\frac{{PD}}{{CD}} \\ $$$$\Rightarrow{BD}×{CD}={PD}^{\mathrm{2}} =\mathrm{12}^{\mathrm{2}} =\mathrm{144} \\ $$

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