If C denotes the circle on AB as diameter, length of tangent from the point (2,6) to C is given

step 1 So in this question if C denotes the circle on AB so if AB as a diameter of circle diameter of c

If C denotes the circle on AB as diameter, length of tangent...

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Key Concepts

Length of Tangent to a Circle

This concept refers to calculating the length of a tangent drawn from an external point to a circle. It is determined using the formula: tangent length = sqrt(d² - r²), where d is the distance from the external point to the center of the circle and r is the radius. This relationship arises because the tangent is perpendicular to the radius at the point of tangency, forming a right-angled triangle.

Power of a Point

The power of a point with respect to a circle is defined as the square of the length of the tangent from that point to the circle. It is also calculated as the difference between the square of the distance from the point to the circle's center and the square of the radius. This concept is useful in solving various problems involving chords, secants, and tangents in circle geometry.

Circle Defined by a Diameter

A circle determined by a diameter is one where the two endpoints of the diameter lie on the circle. An important property of such a circle is that any angle formed at the circumference, subtended by the diameter, is a right angle (Thales’ theorem). This property greatly simplifies many geometric analyses involving circles.

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