Question

in a figure, if LM = MR and angle MLQ = angle MNR = 90°. prove that PQ = PR​

Answer 1

Step-by-step explanation:

HEY MATE ........

$given \: \\ lm \: = mr \: and \: angle \: mlq = < mnr = 90 \: \\ \\ to \: be \: proved \: \\ \\ pq = pr \\ \\ solution \: \\ \\ qm = mr \: \\ in \: triangle \: lmq \: and \: triangle \: mnr \\ \\ lq = \sqrt{ {qm}^{2} } - {ml}^{2} \\ = {mr}^{2} - {mn}^{2} \\ \\ = {nr}^{2} = nr......(1)eqn \\ \\ lq = nr(from \: (1)eqn) \\ \\ qm = mr(given) \\ \\ ml = mn(given) \\ \\ hence \: triangle \: lmq = triangle \: mnr(by \: sss \: rule \: ) \\ \\ lp = ( \sqrt{ {mp}^{2} } - {ml}^{2} ) \\ \\ = ({mp}^{2} - {mn}^{2} ) = \sqrt{ {np}^{2} } = np.......(2) \\ \\ from \: (1) \: and \: (2) \: we \: add \\ \\ lq + lp = rn + np = pq = pr \\ \\ \\ hence \: proved \:$

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