Question

Two circles with centres O and P intersect at A and B as shown in the figure. Prove that
ZAOP= ZBOP.
B В
* ufu for 2

Answer 1

Answer:

Firstly draw two circles with center O and O’ such that they intersect at A and B.

Draw a line PQ parallel to OO’.

In the circle with center O, we have:

OP and OB are the radii of the circle. PB is the chord with OM as its perpendicular bisector.

i.e. BM=MP....(1)

In the circle with center O’, we have:

O’B and O’Q are the radii of the circle. BQ is the chord with O’N as its perpendicular bisector.

i.e. BN=NQ....(1)BM=MP....(1)

From (1) and (2), we have:

BM+BN=MP+NQ

⇒(BM+BN)+(BM+BN)=(BM+BN)+(MP+NQ)

⇒2(BM+BN)=(BM+BN)+(MP+NQ)

⇒2(OO’)=(BM+MP)+(BN+NQ)

⇒2(OO’)=BP+BQ

⇒2OO’=PQ

Answer 2

Step-by-step explanation:

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