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If the median of a triangle through A is...

If the median of a triangle through A is perpendicular to AB, then

A

2tanA+tanB=0

B

2tanA-tanB=0

C

tanA-2tanB=0

D

tanA+2tanB=0

Text Solution

Verified by Experts

In `DeltaABD`, we have
`cosB=(AB)/(BD)`

`rArrcosB=c/(n//2)`
`rArrcosB=(2c)/a`
`rArrcosB=(2sinC)/(sinA)`
`rArr` sin A cos B = 2 sin (A + B)
`0=sinAcosB+ 2 cos A sin B rArr tan A+ 2 tan B=0`
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OBJECTIVE RD SHARMA-PROPERTIES OF TRIANGLES AND CIRCLES CONNECTED WITH THEM-Section I - Solved Mcqs
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  2. ABC is a triangle. D is the middle point of BC. If AD is perpendicular...

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  3. If the median of a triangle through A is perpendicular to AB, then

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  7. If I is the incentre of a DeltaABC such that angleA=60^(@), then AI =

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  11. In a !ABC , if 3a = b + c , then cot B/2 cot C/2 =

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  12. In !ABC , if sin^(2)A/2,sin^(2)B/2,sin^(2)C/2 be in H.P., then a , b ,...

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  13. In a !ABC , if 1/(b+c)+1/(c+a)=3/(a+b+c), then angleC=

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  14. Observe the following statements: (I) In !ABC,bcos^(2)C/2+ccos^(2)B/2=...

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  15. In a triangle , if r(1) = 2r(2) = 3r(3), then a/b + b/c + c/a is equa...

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  16. Sides a , b , c of !ABC are in A.P. and costheta(1)=a/(b+c)costheta(2)...

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  17. Consider a triangle ABC and let a , b , and c denote the lengths of t...

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  18. If the angle A , B and C of a triangle are in arithmetic progession an...

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