Question

In the figure, OA = OB and OP = OQ. Prove that (i) PX = QX (ii) AX = BX​

Answer 1

Answer:

Step-by-steSolution

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It is given that OA=OB and OP=OQ

By considering the △OAQ and △OPB

Therefore, by SAS congruence criterion

△OAQ=△OPB

We know that the corresponding parts of congruent triangles are equal

So we get

∠OBP=∠OAQ..(1)

Consider △BXQ and △PXA

We can write it as

BQ=OB−OQ and PA=OA−OP

We know that OP=OQ and is given that OA=OB

So we get BQ=PA.(2)

In △BXQ and △PXA

We know that ∠BXQ and ∠PXA are vertically opposite angles

∠BXQ=∠PXA

From (1) and (2) and AAS congruence criterion we get

△BXQ≅△PXA

So we get PX=QX and AX=BX(c.p.c.t).p explanation: