Orthogonal Circles Definition
Two circles are defined as orthogonal if they intersect each other. The angle between them is specifically measured at their intersection points.
Angle Calculation
The angle between two intersecting circles is technically the angle formed by their tangents at the point of intersection.
A crucial geometric condition for orthogonality is that the radii drawn from the centers to an intersection point are perpendicular to each other. This geometric property directly defines the angle.
Conclusion
When the radii to the intersection point are perpendicular (forming a 90-degree angle), the tangents at that point are also perpendicular. Therefore, the angle between the two circles is a right angle.
Correct Answer: Option D - right angle
Similar Questions
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- $1^{\circ}$ of latitude is equal to ___ km approximately.
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A park is designed in the shape of a right-angled triangle, where the two shorter sides measure 13 m and 84 m. A circular track with a uniform width of 2 m is constructed such that its outer boundary coincides with the circumcircle of the triangular park. Determine the perimeter of the inner boundary of this circular track.
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Important Questions from Circles
The sum of the radius and diameter of a circle is 84 cm. What is the circumference of this circle?
The maximum area of a right-angled triangle inscribed in a circle of radius r is
The tangent at a point C of a circle and diameter AB when extended intersect at D, if ∠DCA = 110°, then ∠CBA is equal to
The equation of a circle with diameters are 2x - 3y + 12 = 0 and x + 4y - 5 = 0 and area of 154 sq. units is
The internal center of similitude of two circles $ (x - 1)^2 + (y - 3)^2 = 4 $ and $ (x + 5)^2 + (y - 9)^2 = 16 $ is
