Question

23. Two circles with centres O and O' intersect at two points A and B. A line
PQ is drawn parallel to OO' through A or B, intersecting the circles at P
and Q. Prove that PQ = 200'.​

Answer 1

GIVEN :

Two circles with centres O and O' intersect at two points A and B. A linePQ is drawn parallel to OO' through A or B, intersecting the circles at Pand Q.

TO FIND :

• Prove that PQ = 200'.

SOLUTION:

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

Hence, proved.

Answer 2

Answer:

@ananya

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