Question

please help me answer this question.​

Answer 1

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!