Question

PQ is a chord of length 8 cm of a circle of radius 5 cm. The tangents P and Q intersect at a point T. Find the length TP.​

Answer 1

☘️ Solution :

Let the value of TR be x and TP be y cm.

OT is ⊥ bisector of PQ.

So, PR = QR = 4 cm

In ∆ OPR

OP² = PR² + QR²

5² = 4² + QR²

→ QR = 3

In ∆ PRT → y² = x² + 4² ---- (i)

In ∆ OPT → (x + 3)³ = 5² + y²

→ (x + 3)² = 5² + x² + 4² [From eq(i)]

→ x = 16/3 cm

Putting value of x in eq(i)

So, y = 20/3 cm

Therefore, TP = 20/3 cm

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☘️ Answer :

• TP = 20/3