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angle OMP is a right angle. triangle so
OP^2 = OM ^2 + PM^2
100 = OM^2 + 64
OM = 6
let PN = X
AND MN = Y
THEN
IN TRIANGLE PON
(Y+6) ^2 = X^2 + 100
Y^2 + 36 + 12Y = X^2 + 100 .........EQ1
IN TRIANGLE POM
X^2 = Y^2 + 64 .....EQ 2
FROM EQ 1 AND 2
12Y = 128
Y = 128/12 = 32/3
X ^2 = (32/3)^2 + 64
= 1024/ 9 +64
= 1024 + 576 /9
1600/9
X = √1600/9
= 40/3
OP^2 = OM ^2 + PM^2
100 = OM^2 + 64
OM = 6
let PN = X
AND MN = Y
THEN
IN TRIANGLE PON
(Y+6) ^2 = X^2 + 100
Y^2 + 36 + 12Y = X^2 + 100 .........EQ1
IN TRIANGLE POM
X^2 = Y^2 + 64 .....EQ 2
FROM EQ 1 AND 2
12Y = 128
Y = 128/12 = 32/3
X ^2 = (32/3)^2 + 64
= 1024/ 9 +64
= 1024 + 576 /9
1600/9
X = √1600/9
= 40/3
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Answer :- 40/3
Thank You
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