Match the expressions. List I List II (A) If C=90°, find 2(r+R). (P) a+b+c (B) l,m,n are altitudes from A,B,C of triangle with sides a,b,c. Find 2 R ( b l / c + c m / a + an / b ) + 2 ab + 2 b c + 2 c

Question

Match the expressions. List I List II (A) If C=90°, find 2(r+R). (P) a+b+c (B) l,m,n are altitudes from A,B,C of triangle with sides a,b,c. Find 2 R ( b l / c + c m / a + an / b ) + 2 ab + 2 b c + 2 c a ​ . (Q) a-b (C) Find R( b 2 sin2C+ c 2 sin2B). (R) a+b (D) If C=90°, find 4R sin((A+B)/2)sin((A-B)/2). (S) abc

TestHub · Accepted Answer

For C=90°, r=(a+b-c)/2 and R=c/2, giving A=a+b. In B, the first three terms under the radical sum to a 2 + b 2 + c 2 , so B=a+b+c. The sine and cosine rules give C=abc. The product-to-sum formula and sine rule give D=a-b.

Mathematics - Properties of Triangle Question with Solution | TestHub

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Doubts & Discussion

List I	List II
(A) If C=90°, find 2(r+R).	(P) a+b+c
(B) l,m,n are altitudes from A,B,C of triangle with sides a,b,c. Find $2 R (b l / c + c m / a + an / b) + 2 ab + 2 b c + 2 c a$ .	(Q) a-b
(C) Find R( $b^{2}$ sin2C+ $c^{2}$ sin2B).	(R) a+b
(D) If C=90°, find 4R sin((A+B)/2)sin((A-B)/2).	(S) abc