<p>In triangle \(ABC\), \(BQ\) and \(CP\) intersect at \(O\). \(P\), \(Q\), \(R\) and \(S\) are the midpoints of \(AB\), \(AC\), \(OC\) and \(OB\) respectively. Prove that</p>
<div class="graph-block" data-graph-config="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" data-width="217" data-height="150" data-proportional style="width:217px;height:150px;max-width:100%;display:flow-root;margin:0 auto;--graph-width:217px;--graph-aspect:217 / 150;"></div>
<ol class="i-list"><li data-list-item-id="item-i" data-list-item-path="item-i"><div class="list-item-paragraph">\(PQRS\) is a parallelogram,</div></li><li data-list-item-id="item-ii" data-list-item-path="item-ii"><div class="list-item-paragraph">\(OS = \frac{1}{3} BQ\), and</div></li><li data-list-item-id="item-iii" data-list-item-path="item-iii"><div class="list-item-paragraph">\(BS = \frac{1}{3} BQ\).</div></li></ol>

In triangle \(ABC\), \(BQ\) and \(CP\) intersect at \(O\). \(P\), \(Q\), \(R\) and \(S\) are the midpoints of \(AB\), \(AC\), \(OC\) and \(OB\) respectively. Prove that

Proofs in Plane Geometry - Midpoint Theorem

Proofs in Plane Geometry - Midpoint Theorem

Video Solution:

Solution:

Solution locked