In triangle ABC, if the medians AX and BY are mutually perpendicular such that BC2 + AC2=k2(AB2) , where k - Maths - Triangles

Question

In triangle ABC, if the medians AX and BY are mutually
perpendicular such that BC2 +
AC2=k2(AB2) , where k is a real
number , then the value of k can be what?

Lovina Kansal · Accepted Answer

Dear student
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"https://s3mn%20mnimgs%20com/img/shared/ck-files/ck_57f751f17ef1b%20png">
Given: AX and BY are medians
Now ,In △AOB,By Pythagoras Theorem, we haveAB2=OB2+OA2   
(1)In △BOX,By Pythagoras Theorem, we haveBX2=OB2+OX2   ⇒BC24=OB2+OX2     As AX is a median on BC⇒OB2=BC24-OX2     
(2)In △AOY,By Pythagoras Theorem, we haveAY2=OA+OY2   ⇒AC24=OA2+OY2     As BY is a median on AC⇒OA2=AC24-OY2     
(3)In △XOY,By Pythagoras Theorem, we haveXY2=OX2+OY2   
(4)Consider eq(1), we haveAB2=OB2+OA2 ⇒AB2=AC24-OY2  +BC24-OX2 AB2=122AC2+BC2-OX2+OY2    [using 2 and 3]⇒122AB2+XY2=AC2+BC2     [using 4]Please check your question
There is some mistake
Regards

In triangle ABC, if the medians AX and BY are mutually perpendicular such that BC2 + AC2=k2(AB2) , where k is a real number , then the value of k can be what?

In triangle ABC, if the medians AX and BY are mutually perpendicular such that BC² + AC²=k²(AB²) , where k is a real number , then the value of k can be what?