Tangents and Secants to a Circle

A tangent touches the circle at exactly one point, The tangent is perpendicular to the radius at point of contact, Two tangents can be drawn from any external point

A tangent touches circle at one point, is perpendicular to radius at contact point, and exactly two tangents exist from any external point. A tangent cannot pass through the center.

12 cm

For a quadrilateral circumscribing a circle: AB + CD = BC + DA. Substituting: 8 + 10 = 6 + DA. Therefore 18 = 6 + DA, so DA = 12 cm.

77/3 cm²

Area of sector = (θ/360°) × πr². Substituting: Area = (60°/360°) × (22/7) × 7² = (1/6) × (22/7) × 49 = (1/6) × 22 × 7 = 154/6 = 77/3 cm².

275/14 - 25/2 cm²

Area of segment = Area of sector - Area of triangle. Sector area = (90°/360°) × π × 5² = (1/4) × (22/7) × 25 = 275/14 cm². Triangle area = (1/2) × 5 × 5 = 25/2 cm². Segment area = 275/14 - 25/2 cm².