Two circles intersect at P and Q. Through P diameters PA and PB of the two circles are drawn. Show that the points A, Q and B are collinear. - Noon Academy

Two circles intersect at P and Q. Through P diameters PA and PB of the two circles are drawn. Show that the points A, Q and B are collinear.

Circles | Class 10 | Exercise 17A | ICSE | Maths | Selina

Two circles intersect at P and Q. Through P diameters PA and PB of the two circles are drawn. Show that the points A, Q and B are collinear.

Selina Solutions Concise Class 10 Maths Chapter 17 ex. 17(A) - 29

Solution:

According to the given question,

Let

$O\text{ }and\text{ }O$

be the centres of two intersecting circles, where points of the intersection are

$P\text{ }and\text{ }Q\text{ }and\text{ }PA\text{ }and\text{ }PB$

are their diameters respectively.

Join

$PQ,\text{ }AQ\text{ }and\text{ }QB$

Hence,

$\angle AQP\text{ }=\text{ }{{90}^{o}}~and\angle BQP\text{ }=\text{ }{{90}^{o}}$

[Angle in a semicircle is a right angle]

Adding both these angles we get

$\angle AQP\text{ }+\angle BQP\text{ }=\text{ }{{180}^{o}}$

$\angle AQB\text{ }=\text{ }{{180}^{o}}$

Therefore, the points

$A,\text{ }Q\text{ }and\text{ }B$

are collinear.

i

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