Question

৩. একটি ত্রিভুজের পরিব্যাসার্ধ ২৫ সে.মি
এবং অন্তঃ ব্যাসার্ধ ৮ সে.মি দেওয়া আছে।
তাহলে পরিকেন্দ্র ও অন্তঃকেন্দ্রের মধ্যবর্তী
দূরত্ব কতাে? (3. A triangle has a radius
of 25 cm and an inner radius of 8 cm.
So what is the distance between the
center and the inner center?)
আপনার উত্তর​

Answer 1

Given :- A triangle has a outer radius of 25 cm and an inner radius of 8 cm. So what is the distance between the

circum - center and the inner center .

Solution :-

we know that,

• when a circle is formed outside the ∆ touching all vertices with radius R it is called circum - circle and radius of circle is called circum - radius . Centre of this circle is called circumcentre .
• when a circle is formed inside the ∆ touching all sides with radius r it is called in - circle and radius of circle is called in - radius . Centre of this circle is called incentre .
• Distance between circumcentre and incentre of a ∆ is equal to = √[R² - 2•R•r]

Refer to image Now. from image we have :-

• O = circumcentre .
• R = circum - radius.
• I = incentre
• r = inradius .
• d = Distance between O and I .

given that,

• R = 25 cm.
• r = 8 cm.

Putting both values we get,

→ d = √[25² - 2 * 25 * 8]

→ d = √[625 - 400]

→ d = √(225)

→ d = √(15)²

→ d = 15 cm. (Ans.)

Hence, the distance between circum - centre and the inner centre is 15cm.

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