Home
Class 12
MATHS
Let ABC be a triangle inscribed in a cir...

Let ABC be a triangle inscribed in a circle and let `l_(a)=(m_(a))/(M_(a)), l_(b)=(m_(b))/(M_(b)), l_(c )=(m_(c ))/(M_(c ))` where `m_(a), m_(b), m_(c )` are the lengths of the angle bisectors of angles A, B and C respectively , internal to the triangle and `M_(a), M_(b) and M_(c )` are the lengths of these internal angle bisectors extended until they meet the circumcircle.
Q. The maximum value of the product `(l_(a)l_(b)l_(c))xxcos^(2)((B-C)/(2)) xx cos^(2)(C-A)/(2)) xx cos^(2)((A-B)/(2))` is equal to :

A

`(1)/(8)`

B

`(1)/(64)`

C

`(27)/(64)`

D

`(27)/(32)`

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • SOLUTION OF TRIANGLES

    VK JAISWAL ENGLISH|Exercise Exercise-4 : Matching Type Problems|2 Videos

  • SOLUTION OF TRIANGLES

    VK JAISWAL ENGLISH|Exercise Exercise-5 : Subjective Type Problems|9 Videos

  • SOLUTION OF TRIANGLES

    VK JAISWAL ENGLISH|Exercise Exercise-2 : One or More than One Answer is/are Correct|14 Videos

  • SEQUENCE AND SERIES

    VK JAISWAL ENGLISH|Exercise EXERCISE (SUBJECTIVE TYPE PROBLEMS)|21 Videos

  • STRAIGHT LINES

    VK JAISWAL ENGLISH|Exercise Exercise-5 : Subjective Type Problems|10 Videos

Similar Questions

Explore conceptually related problems

Let ABC be a triangle inscribed in a circle and let l_(a)=(m_(a))/(M_(a)), l_(b)=(m_(b))/(M_(b)), l_(c )=(m_(c ))/(M_(c )) where m_(a), m_(b), m_(c ) are the lengths of the angle bisectors of angles A, B and C respectively , internal to the triangle and M_(a), M_(b) and M_(c ) are the lengths of these internal angle bisectors extended until they meet the circumcircle. Q. l_(a) equals :

Let ABC be a triangle inscribed in a circle and let l_(a)=(m_(a))/(M_(a)), l_(b)=(m_(b))/(M_(b)), l_(c )=(m_(c ))/(M_(c )) where m_(a), m_(b), m_(c ) are the lengths of the angle bisectors of angles A, B and C respectively , internal to the triangle and M_(a), M_(b) and M_(c ) are the lengths of these internal angle bisectors extended until they meet the circumcircle. Q. The minimum value of the expression (l_(a))/(sin^(2)A)+(l_(b))/(sin^(2)B)+(l_(c ))/(sin^(2)C) is :

In Figure, A B C is an equilateral triangle. Find m\ /_B E C

A B C D is a parallelogram. L and M are points on A B and D C respectively and A L=C Mdot prove that L M and B D bisect each other.

Let A B C be a triangle with /_B=90^0 . Let AD be the bisector of /_A with D on BC. Suppose AC=6cm and the area of the triangle ADC is 10c m^2dot Find the length of BD.

Let A B C be a triangle with /_B=90^0 . Let AD be the bisector of /_A with D on BC. Suppose AC=6cm and the area of the triangle ADC is 10c m^2dot Find the length of BD.

In figure ABC and AMP are two right triangles, right angles at B and M respectively. Prove that(i) DeltaA B C~ DeltaA M P (ii) (C A)/(P A)=(B C)/(M P)

In triangle A B C ,/_C=(2pi)/3 and C D is the internal angle bisector of /_C , meeting the side A Ba tD . If Length C D is 1, the H.M. of aa n db is equal to: 1 (b) 2 (c) 3 (d) 4

In a right angled triangle A B C , right angled at B ,\ B C=12 c m and A B=5c m . The radius of the circle inscribed in the triangle (in cm) is :

If A B C and A M P are two right triangles, right angled at B and M respectively such that /_M A P=/_B A C . Prove that (C A)/(P A)=(B C)/(M P)