AP EAMCET202315 May 2023Evening ShiftMathematicsStraight LinesActual
If ABC is a right angled isosceles triangle and C =90^ , then r : r ₃=
Options
- A2 +1: 2 -1
- B2 -1: 2 +1
- C2 : 1
- D1: 2
Correct answer
B. 2 -1: 2 +1
Step-by-step solution
A B C is isosceles triangle. A C=B C and C=90^ Let A C=B C a=b In A B C , aligned & c^2=a^2+b^2=a^2+a^2=2 a^2 & c=a 2 aligned Now, r r₃ = s s-c = s-c s aligned & = a+b+c 2 -c a+b+c 2 = a+b-c a+b+c & = a+a-a 2 a+a+a 2 = 2- 2 2+ 2 = 2 -1 2 +1 & r: r₃=( 2 -1):( 2 +1) . aligned