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| 1. |
Ao/Bo=bo/od=1/2 and ab=5cm. find the value of dc |
| Answer» In \u200b{tex}\\triangle {/tex}AOB and \u200b{tex}\\triangle {/tex}\u200bCOD\u200b{tex}\\angle{/tex}\u200b AOB = \u200b{tex}\\angle{/tex}\u200b COD [Vertically opposite angles]{tex}\\frac{{AO}}{{OC}} = \\frac{{BO}}{{OD}} \\Rightarrow \\frac{{AO}}{{OB}} = \\frac{{OC}}{{OD}}{/tex}[Given]\u200b{tex}\\therefore {/tex}\u200b\u200b{tex}\\triangle {/tex}\u200bAOB \u200b{tex} \\sim {/tex}\u200b {tex}\\triangle {/tex}COD [By SAS similarity]\u200b{tex}\\therefore {/tex}\u200b{tex}\\frac{{AO}}{{OC}} = \\frac{{BO}}{{OD}} = \\frac{{AB}}{{CD}}{/tex}{tex}\\frac{1}{2} = \\frac{{AB}}{{DC}}\\left[ {\\frac{{AO}}{{OC}} = \\frac{{BO}}{{OD}} = \\frac{1}{2}} \\right]{/tex}is given\u200b{tex}\\Rightarrow {/tex}\u200b {tex}\\frac{1}{2} = \\frac{5}{{DC}}{/tex}{tex}\\Rightarrow {/tex} DC = 10 cm | |