in figure PQ is a chord of length 16 cm of a circle of radius. The tangentsat P and Q intersect at a point P find the length of TP
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Let the length of TP be Xcm.
In traingle OPM,
OM=√10²-8²
=√100-64
=√36=6cm
Now, In traingle TMP,
TP²=PM²+TM²
X²=8²+TM² .......(ⅰ)
Now,In traingle TPO,
TO²=TP²+PO²
(OM+TM)²=X²+10²
(6+TM)²=X²+100
36+TM²+12TM=X²+100
TM²+12TM=64+TM²+64 (From ⅰ)
12TM=128
TM=128/12
TM=32/3
From (ⅰ),
x²=64+(32/3)²
In traingle OPM,
OM=√10²-8²
=√100-64
=√36=6cm
Now, In traingle TMP,
TP²=PM²+TM²
X²=8²+TM² .......(ⅰ)
Now,In traingle TPO,
TO²=TP²+PO²
(OM+TM)²=X²+10²
(6+TM)²=X²+100
36+TM²+12TM=X²+100
TM²+12TM=64+TM²+64 (From ⅰ)
12TM=128
TM=128/12
TM=32/3
From (ⅰ),
x²=64+(32/3)²
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