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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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NCERT EXEMPLAR-TRIANGLES-Triangles
  1. In figure, if angleBAC=90^(@) and ADbotBC. Then,

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  2. If the diagonals of a rhombus are 12cm and 16cm, find the length of...

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  3. If DeltaABC~DeltaEDF and DeltaABC is not similar to DeltaDEF, then whi...

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  4. If in two DeltaABC and DeltaPQR, (AB)/(QR)=(BC)/(PR)=(CA)/(PQ), then

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  5. In figure, two line segments AC and BD intersects each other at the po...

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  6. In Delta DEF and Delta PQR, it is given that angle D=angle Q and ang...

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  7. In DeltaABC and DeltaDEF, angleB=angleE,angleF=angleC and AB=3DE. Then...

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  8. If DeltaABC~DeltaPQR with (BC)/(QR)=1/3,then (ar(DeltaPRQ))/(ar(DeltaB...

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  9. If DeltaABC~DeltaDFE,angleA=30^@,angleC=50^(@),AB=5 cm,AC=8 cm and DF=...

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  10. If in DeltaABC and DeltaDEF , (AB)/(DE)=(BC)/(FD), then they will be s...

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  11. If DeltaABC~DeltaQRP,(ar(DeltaABC))/(ar(DeltaPQR))=9/4, AB=18 cm and B...

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  12. If S is a point on side PQ of a DeltaPQR such that PS=QS=RS, then

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  13. Is the triangle with sides 25 cm, 5 cm and 24 cm a right triangle? Giv...

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  14. It is given that DeltaDEF~DeltaRPQ. Is it true to say that angleD = an...

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  15. A and B are respectively the points on the sides PQ and PR of a Delta ...

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  16. In figure BD and CE intersect each other at the point P. IsDeltaPBC~De...

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  17. In DeltaPQR and DeltaMST, angleP=55^(@),angleQ=25^(@),angleM=100^(@)an...

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  18. Is the following statement true? Why? "Two quadrilaterals are similar,...

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  19. Two sides and the perimeter of one triangle are respectively three tim...

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  20. If in two right triangles, one of the acute angles of one triangle is ...

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