Observe the following lists If in Δ ABC, R = 
, r = 2 and r 1 = 3 then:
Column- I | Column- II |
(i) Area of triangle | [A] 15 |
(ii) ∠A of triangle | [B] 30 |
(iii) Semi-perimeter of triangle | [C] 90° |
(iv) Largest angle of triangle | [D] 45º |
Text Solution
Verified by Experts(i) [B]; (ii) [C]; (iii) [A]; (iv) [C]
Ans.
(i) [B]
(ii) [C]
(iii) [A]
(iv) [C]
Sol. (i) Applying r 1 r 2 + r 2 r 3 + r 3 r 1 = 
= s 2 and r 1 + r 2 + r 3 = r + 4R
We easily get r 2 = 15, r 3 =10
Area = 
= 30
(ii) Applying r 1 r 2 + r 2 r 3 + r 3 r 1 = 
= s 2 and r 1 + r 2 + r 3 = r + 4R
We easily get r 2 = 15, r 3 =10
Again 
= 
= 
or a = 5
Similarly b = 13, c = 12
⇒ triangle is right angled at A
⇒ A = 90º
(iii) Applying r 1 r 2 + r 2 r 3 + r 3 r 1 = 
= s
2 and r 1 + r 2 + r 3 = r + 4R
We easily get r 2 = 15, r 3 =10
Also S
2 = 
= 15 × 15 ⇒ S = 15
(iv) Applying r 1 r 2 + r 2 r 3 + r 3 r 1 = 
= s 2 and r 1 + r 2 + r 3 = r + 4R
We easily get r 2 = 15, r 3 =10
Again 
= 
= 
or a = 5
Similarly b = 13, c = 12
⇒ triangle is right angled at A
⇒ A = 90º
So largest angle = 90°
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