Question

Please solve this. Class 10 cbse.

Answer 1

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Answer 2

Question :

Find the length of AB from the figure in attachment .

Answer:

$\red{\boxed{\blue{6\frac{2}{3}cm}}}$

Step-by-step explanation:

Given :

PT = 12 cm

OT = 13 cm

Let AD = x .

AP = AD [ Tangents from an external point ]

Hence :

AP = x

So AT = PT - AP

= AT = 12 - x

In Δ ADT ,

∠ADT = ∠PMT = 90

Hence we can apply Pythagoras theorem :

AT² = AD² + DT²

⇒ ( 12  - x )² = 8² + x²

⇒ 144 + x² - 24 x = 8² + x²

⇒ 144 - 24 x = 64

⇒ 24 x = 144 - 64

⇒ 24 x = 80

⇒ x = 80/24

⇒ x = 10/3

The length of AB = AD + DB

Since PT = QT [ Tangent from external point ]

⇒ QB = AP

⇒ DB = AD

Hence AB = AD + AD

= AB = 10/3 + 10/3

= AB = 20/3

The length of AB is $\bf{\frac{20}{3}cm}$