Home
Class 12
MATHS
If circumradius of triangle ABC is 4 cm,...

If circumradius of triangle ABC is 4 cm, then prove that sum of perpendicular distances from circumcentre to the sides of triangle cannot exceed 6 cm

Text Solution

AI Generated Solution

To prove that the sum of the perpendicular distances from the circumcenter to the sides of triangle ABC cannot exceed 6 cm, given that the circumradius \( R \) is 4 cm, we can follow these steps: ### Step-by-Step Solution: 1. **Understand the Given Information**: We know that the circumradius \( R \) of triangle ABC is 4 cm. 2. **Define the Perpendicular Distances**: ...
Promotional Banner

Topper's Solved these Questions

  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE ENGLISH|Exercise Concept application exercise 5.8|7 Videos

  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE ENGLISH|Exercise Concept application exercise 5.9|5 Videos

  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE ENGLISH|Exercise Concept application exercise 5.6|6 Videos

  • PROGRESSION AND SERIES

    CENGAGE ENGLISH|Exercise ARCHIVES (MATRIX MATCH TYPE )|1 Videos

  • RELATIONS AND FUNCTIONS

    CENGAGE ENGLISH|Exercise Archives(Matrix Match Type)|1 Videos

Similar Questions

Explore conceptually related problems

If the sides of triangle are in the ratio 3 : 5 : 7 , then prove that the minimum distance of the circumcentre from the side of triangle is half the circmradius

In equilateral triangle ABC with interior point D, if the perpendicular distances from D to the sides of 4,5, and 6, respectively, are given, then find the area of A B Cdot

A triangle has its sides in the ratio 4:5:6 , then the ratio of circumradius to the inradius of the triangle is

Let a point P lies inside an equilateral triangle ABC such that its perpendicular distances from sides are P_(1),P_(2),P_(3) .If side length of triangle ABC is 2 unit then

A triangle is inscribed in a circle of radius 1. The distance between the orthocentre and the circumcentre of the triangle cannot be

A triangle is inscribed in a circle of radius 1. The distance between the orthocentre and the circumcentre of the triangle cannot be

A triangle is inscribed in a circle of radius 1. The distance between the orthocentre and the circumcentre of the triangle cannot be

Prove that the perpendicular let fall from the vertices of a triangle to the opposite sides are concurrent.

If a triangle is inscribed in a circle, then prove that the product of any two sides of the triangle is equal to the product of the diameter and the perpendicular distance of the thrid side from the opposite vertex.

If the side of an equilateral triangle is 6 cm, then its perimeter is