Question
In the given figure, two circles intersect at two points A and B. AD and AC are diameters to the two circles. Prove that B lies on the line segment DC.
✓
Answer
In the given diagram join AB. Also $\angle ABD =90^{\circ}$ (because angle in a semicircle is always $90^{\circ}$)
Similarly, we have $\angle A B C=90^{\circ}$
So, $\angle ABD +\angle ABC =90^{\circ}+90^{\circ}=180^{\circ}$
Therefore, DBC is a line i.e., B lies on the line segment DC.
Similarly, we have $\angle A B C=90^{\circ}$
So, $\angle ABD +\angle ABC =90^{\circ}+90^{\circ}=180^{\circ}$
Therefore, DBC is a line i.e., B lies on the line segment DC.
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