D Is a Point on the Side BC of a △ABC Such That AD Bisects △BAC. Then

By Team Aakash Byju's | 8th December 2022 BD > BA BA > BD BA = BD BD = CD

Detailed Explanation

[{"selector":"#anim-2db40a8a-bbb6-43dd-a53a-1579a7600244","keyframes":{"opacity":[0,1]},"delay":0,"duration":1200,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}] [{"selector":"#anim-373f515e-8e52-4153-b30b-6c5764509179","keyframes":{"transform":["translate3d(-150.99601%, 0px, 0)","translate3d(0px, 0px, 0)"]},"delay":0,"duration":1200,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}] [{"selector":"#anim-6987036a-e394-4ba6-ba48-59f16b735d27","keyframes":{"opacity":[0,1]},"delay":0,"duration":1200,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}] [{"selector":"#anim-6e220ffc-223c-4f0b-8328-dcf6ab933aba","keyframes":{"transform":["translate3d(-116.66667%, 0px, 0)","translate3d(0px, 0px, 0)"]},"delay":0,"duration":1200,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}] [{"selector":"#anim-523b32d8-88ff-421f-9f0a-6aca386ad570","keyframes":{"opacity":[0,1]},"delay":0,"duration":1200,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}] [{"selector":"#anim-09c9ad44-853d-4ea5-b25e-ac77dc286043","keyframes":{"transform":["translate3d(-361.85568%, 0px, 0)","translate3d(0px, 0px, 0)"]},"delay":0,"duration":1200,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}] Arrow

[{"selector":"#anim-97dc8f6c-a6d3-4910-9db8-946c9e57e7a8","keyframes":{"opacity":[0,1]},"delay":0,"duration":1200,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}] [{"selector":"#anim-e0c95bf9-ca19-4641-9ebd-119963717f97","keyframes":{"transform":["translate3d(-119.10829%, 0px, 0)","translate3d(0px, 0px, 0)"]},"delay":0,"duration":1200,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}] The visualisation of the given case is shown below:

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[{"selector":"#anim-4d3ef8d5-0c34-4d56-873b-8022bd57dbb2 [data-leaf-element=\"true\"]","keyframes":{"transform":["translate(0%, 0%) scale(1.5)","translate(0%, 0%) scale(1)"]},"delay":0,"duration":1500,"easing":"cubic-bezier(.3,0,.55,1)","fill":"forwards"}] Book a Trial Class

[{"selector":"#anim-9a1d0792-fa96-4026-ad49-9af452d15f15","keyframes":{"opacity":[0,1]},"delay":0,"duration":1200,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}] [{"selector":"#anim-17739e11-26b4-40a5-8de3-0c3ce3b5450c","keyframes":{"transform":["translate3d(-115.92356%, 0px, 0)","translate3d(0px, 0px, 0)"]},"delay":0,"duration":1200,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}] [{"selector":"#anim-4678dbd0-26ee-439f-b1be-4f6e7a5e387c","keyframes":{"opacity":[0,1]},"delay":0,"duration":1200,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}] [{"selector":"#anim-322d1078-a103-46f1-8eba-5fa6d37a0fd7","keyframes":{"transform":["translate3d(-123.25581%, 0px, 0)","translate3d(0px, 0px, 0)"]},"delay":0,"duration":1200,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}] [{"selector":"#anim-601decdd-d798-4c82-89d8-bb1f7142f7d8","keyframes":{"opacity":[0,1]},"delay":0,"duration":1200,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}] [{"selector":"#anim-b168b34f-38d4-4ab2-a3a4-a084cd469528","keyframes":{"transform":["translate3d(-115.92356%, 0px, 0)","translate3d(0px, 0px, 0)"]},"delay":0,"duration":1200,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}] We know that the external angle of a triangle is the sum of the opposite internal angles. So, in △ADC ∠ADB = ∠ACD + ∠CAD => ∠ADB > ∠ACD or ∠ADB > ∠CAD

[{"selector":"#anim-a58ea7cc-391e-4b97-a2b4-7c35862a3df8","keyframes":{"opacity":[0,1]},"delay":0,"duration":1200,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}] [{"selector":"#anim-97657578-6cd9-4d88-86de-fb65330e1a53","keyframes":{"transform":["translate3d(-115.92356%, 0px, 0)","translate3d(0px, 0px, 0)"]},"delay":0,"duration":1200,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}] [{"selector":"#anim-469dd400-7409-4eea-9cbf-eba1656c1c70","keyframes":{"opacity":[0,1]},"delay":0,"duration":1200,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}] [{"selector":"#anim-7544b532-afc0-4c00-9fed-58114c8d80d8","keyframes":{"transform":["translate3d(-123.72093%, 0px, 0)","translate3d(0px, 0px, 0)"]},"delay":0,"duration":1200,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}] So we know that ∠BAD = ∠CAD, and ∠ADB > ∠CAD. Thus, we can write: ∠ADB > ∠BAD

[{"selector":"#anim-ef29f163-e4c6-4149-8610-a625acf3a243","keyframes":{"opacity":[0,1]},"delay":0,"duration":1200,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}] [{"selector":"#anim-87e65113-f1d8-4bb3-956e-017ec2bc8715","keyframes":{"transform":["translate3d(-115.92356%, 0px, 0)","translate3d(0px, 0px, 0)"]},"delay":0,"duration":1200,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}] Therefore, in △ABD, ∠ADB > ∠BAD. Also, we know that, in a triangle, the greater angle has the longer side opposite to it.

[{"selector":"#anim-a2691855-3515-47c8-ae5d-aa1909df9689","keyframes":{"opacity":[0,1]},"delay":0,"duration":1200,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}] [{"selector":"#anim-6379da5d-7e11-4763-966e-96c684915145","keyframes":{"transform":["translate3d(-115.92356%, 0px, 0)","translate3d(0px, 0px, 0)"]},"delay":0,"duration":1200,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}] [{"selector":"#anim-1620b8b8-86e2-4612-a21a-9f387d256ff5","keyframes":{"opacity":[0,1]},"delay":0,"duration":1200,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}] [{"selector":"#anim-6511ee60-d52f-490b-9df4-53f5be16090a","keyframes":{"transform":["translate3d(-115.92356%, 0px, 0)","translate3d(0px, 0px, 0)"]},"delay":0,"duration":1200,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}] [{"selector":"#anim-81276c10-4253-471f-ab52-bd9cad2e036f","keyframes":{"opacity":[0,1]},"delay":0,"duration":1200,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}] [{"selector":"#anim-0e186dc4-0a2d-427c-b928-63ee9d9ec0cd","keyframes":{"transform":["translate3d(-116.83501%, 0px, 0)","translate3d(0px, 0px, 0)"]},"delay":0,"duration":1200,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}] The side opposite ∠ADB is BA The side opposite ∠BAD is BD Thus, ∠ADB > ∠BAD => BA > BD

[{"selector":"#anim-53b65e5c-7938-4f83-894c-e2468b8328dc [data-leaf-element=\"true\"]","keyframes":{"transform":["translate(0%, 0%) scale(1.5)","translate(0%, 0%) scale(1)"]},"delay":0,"duration":1500,"easing":"cubic-bezier(.3,0,.55,1)","fill":"forwards"}] Download Aakash App Now

D Is a Point on the Side BC of a △ABC Such That AD Bisects △BAC. Then

A

C

B

D

Detailed Explanation

The correct answer is option B) BA > BD.

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