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Question

In the given figure, AP = AQ and the right angles are shown. Which of the following statements can certainly be stated?


A

AP = PB

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B

AB = AC

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C

AQ = AD

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D

None of these

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Solution

The correct option is B

AB = AC


Since PB, AD and QC are perpendicular to the same line BC, they are parallel to each other i.e. PB || AD || QC.
Since, PB || AD || QC and PQ is a transversal making equal intercepts i.e. PA = AQ; therefore the other transversal BC will also make equal intercepts i.e. BD = CD.
Now in ΔABD and ΔACD.
(i) BD = CD [Proved above]
(ii) AD = AD [Common]
(iii) ADB=ADC=90 [As, AD BC]
ΔABD=ΔACD [By SAS]
AB = AC [By C.P.C.T]


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