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Question

 Mark the correct alternative in each of the following :

The acute angle between the medians drawn from the acute angles of a right angled isosceles triangle is



A

cos1(23)

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B

cos1(34)

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C

cos1(45)

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D

cos1(56)

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Solution

The correct option is C

cos1(45)


Let the coordinates of the right-angled isosceles triangle be O(0, 0), A(a, 0) and B(0, a)

Here, BD and AE are the medians drawn from the acute angles B and A, respectively.

Slope of BD = m1

=0αα20

=2

Slope of AE = m2

=α200α

=12

Let θ be the angle between BD and AE

tan θ=2+121+1

=34

    cos θ=432+44

    cos θ=45

    θ=cos1(45)

Hence, the acute angle between the medians is cos1(45)


Mathematics
RD Sharma
Standard XI

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