In a triangle ABC , let angle C = 90o If r is the inradius and R is - Maths - Trigonometric Functions

Question

In a triangle ABC , let angle C = 90o If r is the
inradius and R is the circumradius , then 2(r + R) is equal to
a) a+b
b) b+c
​c) a+c
d) a+b+c

Priyanka Kedia · Accepted Answer

Dear Student,

Given, In a triangle ABC,∠C=900We know that,R=c2sinC⇒R=c2sin900⇒R=c2⇒2R=c        
1And,r=s-ctanC2⇒r=s-ctan9002⇒r=s-ctan450⇒r=s-c⇒2r=2s-2c        
2Adding equation1 and 2, we have,2R+2r=c+2s-2c⇒2R+2r=c+a+b+c-2c⇒2R+2r=a+b⇒2R+r=a+b

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In a triangle ABC , let angle C = 90o . If r is the inradius and R is the circumradius , then 2(r + R) is equal to a) a+b b) b+c ​c) a+c d) a+b+c

In a triangle ABC , let angle C = 90^o . If r is the inradius and R is the circumradius , then 2(r + R) is equal to
a) a+b
b) b+c
c) a+c
d) a+b+c