Home
Class 12
MATHS
The exradii r(1), r(2), and r(3) " of " ...

The exradii `r_(1), r_(2), and r_(3) " of " Delta ABC` are in H.P. show that its sides a, b, and c are in A.P.

Text Solution

Verified by Experts

`r_(1), r_(2),r_(3)` are in H.P
`rArr 1//r_(1), 1//r_(2), 1//r_(3)` are in A.P
`rArr (s -a)/(Delta), (s -a)/(Delta), (s-c)/(Delta)` are in A.P
`rArr s -a, s - b, s -c` are in A.P
Promotional Banner

Topper's Solved these Questions

  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE|Exercise Exercise 5.11|4 Videos

  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE|Exercise Exercise (Single)|80 Videos

  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE|Exercise Exercise 5.9|5 Videos

  • PROGRESSION AND SERIES

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

  • PROPERTIES OF TRIANGLE, HEIGHT AND DISTANCE

    CENGAGE|Exercise Question Bank|32 Videos

Similar Questions

Explore conceptually related problems

The exradii r_(1),r_(2) and r_(3) of /_ABC are in H.P.Show that its sides a,bandc are in AP .

The exradii r_(1), r_(2), r_(3)" of "DeltaABC and in HP, show that it’s the arithmetic mean of a and c.

If in Delta ABC , sides a, b, c are in A.P. then

The radii r_(1), r_(2), r_(3) of the escribed circles of the triangle ABC are in H.P. If the area of the triangle is 24 cm^(2) and its perimeter is 24 cm, then the length of its largest side is

If r_(1), r_(2), r_(3) in triangle be in H.P., then the sides are :

The radii r_(1),r_(2),r_(3) of the escribed circles of the triangle ABC are in H.P.If the area of the triangle is 24cm^(2) and its perimeter is 24cm, then the length of its largest side is 10 (b) 9 (c) 8 (d) none of these

The ex-radii of a triangle r_(1),r_(2),r_(3) are the hamonic progression ,then the sides a,b,c are