Prove that the radii of two equal intersecting circles, drawn to the point of their intersection, form equal angles with a common chord.
| November 27, 2020 | education
Given:
Two circles in which:
О1 and О2 – centers
R – radii (equal)
Prove: ∠1 = ∠3.
Decision:
Since the radii of the circles are equal (by condition), then the circles themselves are equal.
This means that AB is the axis of symmetry of triangles ABO1 and ABO2, since the distances from the points are equal.
Based on this, we know that by definition of symmetry, the figures are equal.
So the angles are also equal.
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