Circle
- In the adjoining figure, seg QR is a chord of the circle with centre O. P is the midpoint of the chord QR. Theorems which are useful to find solution: i. The segment joining the centre of a circle and the midpoint of a chord is perpendicular to th... 1
- What is the distance between two parallel tangents of a circle having radius 4.5 cm? Justify your answer. Let the lines PQ and RS be the two parallel tangents to circle at M and N respectively. Through centre O, draw line AB || line RS. OM = ON =... 1
- Seg RM and seg RN are tangent segments of a circle with centre O. Prove that seg OR bisects ∠MRN as well as ∠MON. Proof: In ∆OMR and ∆ONR, seg RM ≅ seg RN [Tangent segment theorem] seg OM ≅ seg ON [Radii of the same circle] seg OR ≅ seg OR [Common side]... 1
- In the adjoining figure, O is the centre of the circle. From point R, seg RM and seg RN are tangent segments seg RM and seg RN are tangents to the circle with centre O. [Given] ∴ ∠OMR = ∠ONR = 90° [Tangent theorem] i. In ∆OMR, ∠OMR = 90° ∴ OR2 = OM2... 1
- In the adjoining figure, the radius of a circle with centre C is 6 cm, line AB is a tangent at A. i. line AB is the tangent to the circle with centre C and radius AC. [Given] ∴ ∠CAB = 90° (i) [Tangent theorem] ii. seg CA ⊥ line AB [From (... 2