Question - Geometry Problem: Tangents to a Circle
Solution:
The image displays a geometric shape with a circle inside a triangle. The side lengths of the triangle are given: JL is 10 units, LM is 7 units, and KM is 4 units. The segment JK, which is not part of the triangle, is tangent to the circle at point L.To solve for JK, we can use the properties of a tangent to a circle. A tangent to a circle is perpendicular to the radius at the point of tangency. In this case, since KL is a tangent to the circle at point L, KL is perpendicular to any radius from the circle that ends at L.Since KM is also a tangent to the circle and meets the other tangent JL at point K, the lengths of two tangents drawn from the same external point to a circle are equal. Therefore, the lengths of KL and KM are equal because they are both tangents from point K to the circle.Given that KM is 4 units, KL must also be 4 units.Thus, JK is the sum of the lengths of JL and KL, which is 10 units + 4 units, equalling to 14 units.Therefore, JK equals 14 units.
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