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In figure, if angleBAC=90^(@) and ADbotB...

In figure, if `angleBAC=90^(@)` and `ADbotBC`. Then,

A

`BD.CD=BC^(2)`

B

`ABcdotAC=BC^(2)`

C

`BDcdotCD=AD^(2)`

D

`ABcdotAC=AD^(2)`

Text Solution

Verified by Experts

The correct Answer is:
C
Ib `DeltaADB` and `DeltaADC`,

`angled=angleD=90^(@)`
`angleDBA=angleDAC` [each equal to `90^(@)- ltC`]
`thereforeDeltaADB~DeltaADC` [by AAAsimilarity criterion]
`therefore(BD)/(AD)=(AD)/(CD)`
`rArrBDcdotCD=AD^(2)`
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Knowledge Check

  • In the figure, if angleBAC = 90^(@) and AD bot BC , then:

    A
    `BD.CD = BC^(2)`
    B
    `AB.AC = BC^(2)`
    C
    `BD.CD = AD^(2)`
    D
    `AB.AC = AD^(2)`

  • In the figure given below angleBAC=90^(@) and AD bot BC. Then

    A
    `BCxx CD= AC^(2)`
    B
    `AB xx AC =BC^(2)`
    C
    `BDxx CD =AD^(2)`
    D
    `AB xx AC=AD^(2)`

  • In figure, if angleAOB=90^(@) and angleABC=30^(@)," then" angleCAO is equal to

    A
    `30^(@)`
    B
    `45^(@)`
    C
    `90^(@)`
    D
    `60^(@)`

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