Given from the figure let’s consider
Using Pythagoras theorem,
[tex]\huge\mathcal{\fcolorbox{lavender}{lavender}{\pink{ᎪղՏωᎬя᭄}}}[/tex]
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[tex]△LOP \: and \: △MOP[/tex]
We can observe that,
[tex]\begin{gathered}∠L=∠M ….both \: are \: \\ right \: angles \: \\ \end{gathered} [/tex]
[tex]\begin{gathered}⇒∠O=∠O\\ \\ ( common \: angle)\end{gathered} [/tex]
[tex]\begin{gathered}Thus \: by \: AA \: test \\ \\ △LOP≅△MOP\end{gathered} [/tex]
So we can say that LP=MP Elements of congruent triangles
Now we will find the value of LP.
[tex]From \: △LOP \: ,[/tex]
[tex]\begin{gathered}LP= \sqrt{(OP) {}^{2} - (OL ){}^{2} } \\ \end{gathered} [/tex]
Putting the values from the figure,
[tex]\begin{gathered}LP = \sqrt{( {5)}^{2} - ( {3)}^{2} } \\ \\ LP = \sqrt{25 - 9} \\ \\ LP = \sqrt{16} \\ \\ LP = 4 \: cm\end{gathered} [/tex]
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Answers & Comments
Given from the figure let’s consider
[tex]△LOP \: and \: △MOP[/tex]
[tex]∠L=∠M ….both \: are \: \\ right \: angles \: \\ [/tex]
[tex]⇒∠O=∠O\\ \\ ( common \: angle)[/tex]
[tex]Thus \: by \: AA \: test \\ \\ △LOP≅△MOP[/tex]
[tex]From \: △LOP \: ,[/tex]
Using Pythagoras theorem,
[tex]LP= \sqrt{(OP) {}^{2} - (OL ){}^{2} } \\ [/tex]
[tex]LP = \sqrt{( {5)}^{2} - ( {3)}^{2} } \\ \\ LP = \sqrt{25 - 9} \\ \\ LP = \sqrt{16} \\ \\ LP = 4 \: cm[/tex]
[tex]\huge\mathcal{\fcolorbox{lavender}{lavender}{\pink{ᎪղՏωᎬя᭄}}}[/tex]
—♡—♡—♡—♡—♡—♡—♡—
Given from the figure let’s consider
[tex]△LOP \: and \: △MOP[/tex]
We can observe that,
[tex]\begin{gathered}∠L=∠M ….both \: are \: \\ right \: angles \: \\ \end{gathered} [/tex]
[tex]\begin{gathered}⇒∠O=∠O\\ \\ ( common \: angle)\end{gathered} [/tex]
[tex]\begin{gathered}Thus \: by \: AA \: test \\ \\ △LOP≅△MOP\end{gathered} [/tex]
So we can say that LP=MP Elements of congruent triangles
Now we will find the value of LP.
[tex]From \: △LOP \: ,[/tex]
Using Pythagoras theorem,
[tex]\begin{gathered}LP= \sqrt{(OP) {}^{2} - (OL ){}^{2} } \\ \end{gathered} [/tex]
Putting the values from the figure,
[tex]\begin{gathered}LP = \sqrt{( {5)}^{2} - ( {3)}^{2} } \\ \\ LP = \sqrt{25 - 9} \\ \\ LP = \sqrt{16} \\ \\ LP = 4 \: cm\end{gathered} [/tex]
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