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CBSE Class 10 Answered

In a triangle PQR, S and T is a point on PQ and PR respectively such that SR is parallel to QR. Show that RT(PQ+PS)=SQ(PR+PT).
Asked by rushabhjain.avv | 24 Jan, 2019, 06:38: PM
answered-by-expert Expert Answer
ST is parallel to QR.(as posted in question, SR can not be parallel to QR)
 
since ST is paralel to QR, ΔPST and ΔPQR are similar triangles.
 
Hence begin mathsize 12px style fraction numerator P Q over denominator P S end fraction space equals space fraction numerator P R over denominator P T end fraction end style
By compenendo and dividendo,
begin mathsize 12px style fraction numerator P Q plus P S over denominator P Q minus P S end fraction space equals space fraction numerator P R plus P T over denominator p R minus P T end fraction i. e. comma space fraction numerator P Q plus P S over denominator S Q end fraction equals fraction numerator P R plus P T over denominator T R end fraction i. e. comma space T R left parenthesis P Q plus P S right parenthesis space equals space S Q left parenthesis P R plus P T right parenthesis end style
Answered by Thiyagarajan K | 24 Jan, 2019, 10:13: PM

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