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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

$$inthisfigurePQ\mid \mid BAandPR\mid \mid CA$$$$ifPD=12findBD\times CD$$

Answered by MrW3 last updated on 21/Sep/18

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

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