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Answer:
Length of TP = 20/3 cm
Step-by-step explanation:
According to question, radius, OP = 5 cm
Length of chord, PQ = 4 cm
Since ,OT ⊥ PQ, we know that perpendicular drawn to the chord bisects the chord,so
PR = RQ = 4 cm
Now ,Using pythagoras theorem for ΔOPR,
OP² = PR² + OR²
⇒ 25 = 16 + OR²
⇒ OR² = 25 – 16 = 9
Hence OR = 3 cm
Similarly in ΔPTR,
PT² = TR² + PR² ----- (1)
∠OPT = 90º since radius is perpendicular to tangent at point of contact
In right ΔOPT,
OT² = PT² + OP² ----- (2)
From equations (1) and (2), we get
TR= 16/3 cm
Putting the value in eq(1),
PT² = TR² + PR²
= 256/9 + 16
=(256 + 144)/9
= (400/9)
PT = 20/3 cm
Hope This Helps You!