Question

tangents drawn from an external point p touches circle (o,5) at t.if op intersects circle at b and pt=12 then find bt

Answer 1

Answer:

Step-by-step explanation:

If tangent is drawn through a circle by 0,5 then it is not a bt s

olution

Answer 2

tangents drawn from an external point p touches circle (o,5) at t.

Consider the attached figure while going through the following steps.

From figure, we have,

OP² = OT² + PT²

= 5² + 12²

= 160

∴ OP = 13 cm

we have, OP = PB + BO

13 = PB + 5

∴ PB = 8 cm.

In Δ OTP,

cos POT = OT/OP = 5/13

⇒ cos BOT = 5/13

Therefore, using cosine rule we have,

∴ BT² = OB² + OT² - 2 × OB × OT cos BOT

= 5² + 5² - 2 × 5 × 5 × 5/13

= 25 + 25 - 250/13

= 50 - 250/13

= 400/13

⇒ BT = √ (400/13)

∴ BT = 20/√13