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PQ is a chord of length 8 cm, of a circle with centre O and of radius 5 cm. The tangents at P and Q intersect at a point T. The length of TP is
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20 cm. 3 -
21 cm. 4 -
10 cm. 3 -
15 cm. 4
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Correct Option: A
As per the given in question , we draw a figure of a circle with centre O, 
OT is the perpendicular bisector of chord PQ.
Let TR = y
∴ PR = QR = 4 cm
In right angle ∆ ORP,
OP² = OR² + PR²
⇒ OR² = OP² – PR² = 5² – 4² = 9
⇒ OR = 3 cm
In right angled ∆ PRT and ∆ OPT,
TP² = TR² + PR² and OT² = TP² + OP²
⇒ OT² = TR² + PR² + OP²
⇒ (y + 3)² = y² + 16 + 25
| ⇒ 6y = 32 ⇒ y = | |
| 3 |
| ∴ TR = | |
| 3 |
| ∴ TP² = TR² + PR² = |  |  | ² | + 16 | |
| 3 |
| TP² = | + 16 = | ||
| 9 | 9 |
| ∴ TP = | cm. | |
| 3 |
