ConstructionModerate2 marks
8(b)
Draw a line AB = 5 cm. Mark a point C on AB such that AC = 3 cm. Using a ruler and a compass only, construct :
Construct two tangents to the circle from the external point B. Measure and record the length of the tangents.
Topic: Tangents / intersecting chords
Previous-year question practice database
Answer
Solution diagram
Exam answer
From external point B:
- Join BO, where O is the centre of the circle.
- Construct the midpoint M of BO.
- With M as centre and radius MB, draw a circle cutting the given circle at T₁ and T₂.
- Join BT₁ and BT₂.
BT₁ and BT₂ are the required tangents.
Measure: BT₁ = BT₂ ≈ 4.3 cm.
Answer:
Each tangent is approximately 4.3 cm.
Explanation
A tangent from an external point is perpendicular to the radius at the point of contact. The auxiliary circle with diameter BO produces right angles at T₁ and T₂, so BT₁ and BT₂ are tangents. Tangents from the same external point are equal.