File: /var/www/content-sp/wiris-formulas/11e855b4441bf861f2cf4c99c3227391.ini
mml=<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Since</mi><mo>,</mo><mi mathvariant="normal"> </mi><mi>the</mi><mi mathvariant="normal"> </mi><mi>angle</mi><mi mathvariant="normal"> </mi><mi>of</mi><mi mathvariant="normal"> </mi><mi>the</mi><mi mathvariant="normal"> </mi><mi>elevation</mi><mi mathvariant="normal"> </mi><mi>of</mi><mi mathvariant="normal"> </mi><mi>the</mi><mi mathvariant="normal"> </mi><mi>top</mi><mi mathvariant="normal"> </mi><mi>of</mi><mi mathvariant="normal"> </mi><mi>the</mi><mi mathvariant="normal"> </mi><mi>pole</mi><mi mathvariant="normal"> </mi><mi>are</mi><mi mathvariant="normal"> </mi><mi>same</mi><mi mathvariant="normal"> </mi><mi>from</mi><mi mathvariant="normal"> </mi><mi>each</mi><mi mathvariant="normal"> </mi><mi>corner</mi><mi mathvariant="normal"> </mi><mi>of</mi><mi mathvariant="normal"> </mi><mo>∆</mo><mi>ABC</mi><mo>.</mo><mspace linebreak="newline"/><mo>∴</mo><mi mathvariant="normal"> </mi><mi>In</mi><mi mathvariant="normal"> </mi><mo>∆</mo><mi>AOP</mi><mo>,</mo><mi mathvariant="normal"> </mi><mi>tanα</mi><mi mathvariant="normal"> </mi><mo>=</mo><mfrac><mi>OP</mi><mi>OA</mi></mfrac><mo>  </mo><mo>  </mo><mo>  </mo><mo> </mo><mo> </mo><mo> </mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>(</mo><mi mathvariant="normal">i</mi><mo>)</mo><mspace linebreak="newline"/><mi>In</mi><mi mathvariant="normal"> </mi><mo>∆</mo><mi>BOP</mi><mo>,</mo><mi mathvariant="normal"> </mi><mi>tanβ</mi><mi mathvariant="normal"> </mi><mo>=</mo><mfrac><mi>OP</mi><mi>OB</mi></mfrac><mo>  </mo><mo>  </mo><mo>  </mo><mo>  </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>(</mo><mi>ii</mi><mo>)</mo><mspace linebreak="newline"/><mi>In</mi><mi mathvariant="normal"> </mi><mo>∆</mo><mi>COP</mi><mo>,</mo><mi mathvariant="normal"> </mi><mi>tanγ</mi><mi mathvariant="normal"> </mi><mo>=</mo><mfrac><mi>OP</mi><mi>OC</mi></mfrac><mo>  </mo><mo>  </mo><mo>  </mo><mo>  </mo><mo>  </mo><mi mathvariant="normal"> </mi><mo>.</mo><mo>.</mo><mo>.</mo><mo>(</mo><mi>iii</mi><mo>)</mo><mspace linebreak="newline"/><mo>∵</mo><mi mathvariant="normal"> </mi><mi mathvariant="normal">α</mi><mi mathvariant="normal"> </mi><mo>=</mo><mi mathvariant="normal"> </mi><mi mathvariant="normal">β</mi><mi mathvariant="normal"> </mi><mo>=</mo><mi mathvariant="normal"> </mi><mi mathvariant="normal">γ</mi><mspace linebreak="newline"/><mo>∴</mo><mi mathvariant="normal"> </mi><mi>OA</mi><mi mathvariant="normal"> </mi><mo>=</mo><mi mathvariant="normal"> </mi><mi>OB</mi><mi mathvariant="normal"> </mi><mo>=</mo><mi mathvariant="normal"> </mi><mi>OC</mi><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo>[</mo><mi>given</mi><mo>]</mo><mspace linebreak="newline"/><mi>Hence</mi><mo>,</mo><mi mathvariant="normal"> </mi><mi mathvariant="normal">O</mi><mi mathvariant="normal"> </mi><mi>is</mi><mi mathvariant="normal"> </mi><mi>the</mi><mi mathvariant="normal"> </mi><mi>circumcentre</mi><mi mathvariant="normal"> </mi><mi>of</mi><mi mathvariant="normal"> </mi><mo>∆</mo><mi>ABC</mi><mo>.</mo></math>