Relation between Inradius and Perimeter of Triangle
ABC is a righ...
Question
ABC is a right-angled triangle with AC = 65 cm and ∠B=90∘ If r = 7 cm if area of triangle ABC is abc (abc is three digit number) then (a−c) is
A
1
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B
0
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C
2
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D
3
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Solution
The correct option is A 1 r=7 cm and R=AC/2sinB=32.5 cm; Again using r=4RsinA2sinB2sinC2 ⇒r=R[cosA+cosB+cosC−1]⇒cosA+cos90∘+cos(90∘−A)−1=732.5 ⇒cosA+sinA=39.532.5=7965 ⇒sin2A=792−652652 Now △=2R2sinAsinC=R2sin2A=(652)2×792−652652=144×144=72×7=504 sq.units