Question

In triangle ABC,right angl at c,P&Q are the mid points of CA&CB then prove that 4AQ^2=4AC^2+BC^2

Answer 1

here cq =1/2×BC

in triangle ACQ ,

${aq}^{2} = {ac}^{2} + {cq}^{2} \\ = > {aq}^{2} = {ac}^{2} + { (\frac{bc}{2} )}^{2} \\ = > {aq}^{2} = {ac}^{2} + \frac{bc}{4} \\ = > {aq}^{2} = \frac{4 {ac}^{2} + {bc}^{2} }{4}$

$= > {4aq}^{2} = {4ac}^{2} + {bc}^{2}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: ...hence \: prove$

$mark \: as \: brainlist$