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In the figure, two circles intersect eac...

In the figure, two circles intersect each other at points `A` and `B`. `AP` and `AQ` are the diameters of these circles. Prove that `PBQ` is a straight line.

Text Solution

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Join `AB`.
In first circle,
`AP` is the diameter of the circle.
`therefore angle ABP=90^@` (angle in a semi-circle)
In second circle,
`AQ` is the diameter of the circle.
`therefore angle ABQ=90^@`
Now, `angleABP+angle ABQ=90^@+90^@`
`rArrangle PBQ=180^@`
`rArrPBQ` is a straight line.
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