Lines TP and TQ are tangents drawn from an external point to the circle. If the line that intersects at the middle point of PQ from T is 4 cm, and the length of the chord is 2 cm. Find the area of the circle.
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Area of circle = 17 π /16 cm² = 3.34 cm²
Step-by-step explanation:
Let say middle point of PQ = M
& center of circle = O
TM = 4 cm
PM = QM = PM/2 = 2/2 = 1 cm
TP² = TM² + PM²
=> TP² = 4² + 1²
=> TP² = 17
Let say OM = x
OP = Radius
Then OP² = OM² + PM²
=> OP² = x² + 1²
=> OP² = x² + 1
OT² = OP² + TP²
=> (OM + TM)² =x² + 1 + 17
=>(x + 4)² = x² + 18
=> x² + 16 + 8x = x² + 18
=> 8x = 2
=> x = 1/4
OP² = (1/4)² + 1
=> OP²= 17/16
Area of circle = π Radius²
= π * (17/16)
= 17 π /16 cm²
= 3.34 cm²
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