Question
Download Solution PDFThe product of the perimeter of a triangle, the radius of its in‐circle, and a number gives the area of the triangle. The number is
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
- Incircle of a triangle is a circle which is inscribed by the triangle.
- Area of a triangle =
× base × height.
Calculation:
Consider a triangle ABC with incircle with radius r.
∴ OF = OH = OG = r.
Consider Δ ABO.
Here OF is perpendicular to AB (AB is tangent to the circle)
Area of Δ ABO =
⇒ Area of Δ ABO =
Similarly
Area of Δ ACO =
⇒ Area of Δ ABO =
Similarly
Area of Δ OBC =
⇒ Area of Δ ABO =
Area of Δ ABC = Area of Δ ABO + Area of Δ ACO + Area of Δ OBC
⇒ Area of Δ ABC =
⇒ Area of Δ ABC =
⇒ Area of Δ ABC =
Hence the number is 1/2
Last updated on Jun 5, 2025
-> The NTA has released the CSIR NET 2025 Notification for the June session.
-> The CSIR NET Application Form 2025 can be submitted online by 23rd June 2025
-> The CSIR UGC NET is conducted in five subjects -Chemical Sciences, Earth Sciences, Life Sciences, Mathematical Sciences, and Physical Sciences.
-> Postgraduates in the relevant streams can apply for this exam.
-> Candidates must download and practice questions from the CSIR NET Previous year papers. Attempting the CSIR NET mock tests are also very helpful in preparation.