1. Class 10
2. Important Questions for Exam - Class 10
3. Chapter 11 Class 10 Constructions

Transcript

Let ABC be a right triangle in which AB = 6 cm, BC = 8 cm and ∠ B = 90°. BD is the perpendicular from B on AC. The circle through B, C, D is drawn. Construct the tangents from A to this circle. Given AB = 6 cm, BC = 8 cm and ∠ B = 90° and BD is perpendicular from B on AC. We draw circle through B, C, D Now, ∠ BDC = 90° Since ∠ BDC is angle formed by chord BC in circle & its 90° ∴ BC is the diameter of circle. Thus, center of circle will be the bisector of line BC Steps of construction Bisect line BC. Let E be mid-point of BC. Thus, E is center of circle. We need to construct tangents from point A to the circle Join line AE and bisect it. Let M be mid point of AE Taking M as centre and AM as radius, draw a circle. Let it intersect the given circle at points B and P. Join AB and AP. Thus, AB and AP are the required tangents Justification: We need to prove that AG and AB are the tangents to the circle. Join EP. APE is an angle in the semi-circle of the blue circle And we know that angle in a semi-circle is a right angle. ∴ ∠EPA = 90° ⇒ OQ ⊥ PQ Since EP is the radius of the circle, AP has to be a tangent of the circle. Also, given ∠ B = 90° Since EB is the radius of the circle, AB is a tangent of the circle.

Chapter 11 Class 10 Constructions

Class 10
Important Questions for Exam - Class 10