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CBSE Class 10 Answered

Please prove it! 
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Asked by st.mausamraj | 27 Jan, 2019, 08:52: PM
answered-by-expert Expert Answer
ΔPXZ and ΔQXZ are right-angled triangles.
 
begin mathsize 12px style angle end stylePXZ = 90-begin mathsize 12px style angle end styleQXZ 
begin mathsize 12px style angle end styleXQZ = 90-begin mathsize 12px style angle end styleQXZ
hence begin mathsize 12px style angle end stylePXZ = begin mathsize 12px style angle end styleXQZ and ΔPXZ and ΔQXZ are similar triangles.
since begin mathsize 12px style angle end stylePXZ = begin mathsize 12px style angle end styleXQZ, we have PZ = k(XZ) ................(1)
similarly begin mathsize 12px style angle end styleXPZ = begin mathsize 12px style angle end styleQXZ, we have XZ = k(ZQ) ..............(2)
By dividing eqn.(1) by eqn.(2), we get begin mathsize 12px style fraction numerator P Z over denominator X Z end fraction space equals space fraction numerator X Z over denominator Z Q end fraction space o r space space space space space X Z squared space equals space P Z space cross times space Z Q end style
Answered by Thiyagarajan K | 27 Jan, 2019, 10:49: PM
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