Question

In the figure, the circle with centre A and
radius 18 touches the circle with centre C and radius 5 at point M radius AN of the large circle touchez the smaller circle in the T find AT​

Answer 1

Solution :-

given that,

→ AM (Radius of bigger circle) = 18 unit .

→ CM = CT = 5 unit (Radius of smaller circle.)

So, In ∆ACT we have,

→ AM - CM = 18 - 5

→ AC = 13 units .

Now, in the given figure, seg AN is tangent to the circle with centre C at point T .

So,

→ ∠CTA = 90°

therefore, in right ∆CTA we have,

→ AT = √[AC² - CT²) { By pythagoras theorem. }

→ AT = √(13² - 5²)

→ AT = √(169 - 25)

→ AT = √(144)

→ AT = 12 units . { Taking positive value only. }

Hence, value of AT is equal to 12 units .

Learn more :-

*एक वृत्त पर एक बिंदु Q से खींची गयी स्पर्श रेखा की लंबाई 24 सेमी है तथा Q की केंद्र से दूरी 25 सेमी है। वृत्त की त्रिज्...

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यदि एक छात्र एक वृत्त को चार बराबर भागों में विभाजित करता है तो वह होगा

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Answer 2

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