In triangle ABC, the line joining the circumcenter and incenter is parallel to side AC, then `cos A + cos C` is equal to

Question

In triangle ABC, the line joining the circumcenter and incenter is parallel to side AC, then `cos A + cos C` is equal to

In triangle ABC, the line joining the circumcenter and incenter is parallel to side AC, then `cos A + cos C` is equal to
A. `(1)/(2)`
B. 1
C. `sqrt3`
D. 2

Monjur Alahi

6 views

2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Salim Ahmed Kawsar

Correct Answer - B
The distance of circumcenter from side AC is `R cos B`, and the distance of incenter from side AC is r. Therefore,
`R = cos B = r " or " (r)/(R) = cos B`
`rArr 4 sin.(A)/(2) sin.(B)/(2) sin.(C)/(2) = cosB`
`rArr cosA + cos B + cos C - 1 = cos B`
or `cos A + cos C = 1`

6 views Answered 2023-02-05 15:29