LIWA

Circles

CBSE Class 10 · Maths · Chapter 10

Past board exam questions

CBSE 2027 sample paper · 1 mark

The diameter of a car wheel is 21 cm. The number of complete revolutions it will make in moving 66 km is:

  1. 104
  2. 105
  3. 106
  4. 107
Show answer
105

CBSE 2027 sample paper · 1 mark

The length of a tangent drawn from a point at a distance of 10 cm from the centre of the circle is 8 cm. The radius of the circle is

  1. 4 cm
  2. 5 cm
  3. 6 cm
  4. 7 cm
Show answer
6 cm

CBSE 2027 sample paper · 1 mark

The arc of a circle is of length 6π cm and the sector it bound has an area of 24π cm². The radius of the circle is:

  1. 4 cm
  2. 8 cm
  3. 16 cm
  4. 18 cm
Show answer
8 cm

CBSE 2027 sample paper · 1 mark

If tangents PA and PB from a point P to a circle with centre O and respective point of contacts as A and B, are inclined to each other at angle of 80°, then ∠AOB is equal to

  1. 60°
  2. 70°
  3. 80°
  4. 100°
Show answer
100°

CBSE 2027 sample paper · 2 marks

PA is a common tangent and QB and PC are the tangents from Q and P to the smaller and larger circle respectively. If QB = 5cm and PC = 9cm, then evaluate length of PQ. (The two circles touch each other internally at A, the smaller circle, with centre O, lying inside the larger one; PA is their common tangent at A. Q lies on the tangent between A and P. QB touches the smaller circle at B and PC touches the larger circle at C.)

Show answer
Lengths of tangents from an external point to a circle are equal. From Q to the smaller circle: QA = QB = 5 cm. From P to the larger circle: PA = PC = 9 cm. PQ = PA − QA = 9 cm − 5 cm = 4 cm.

CBSE 2027 sample paper · 2 marks

Find the area of a sector of a circle with diameter 28 cm, If the length of the corresponding arc is 22 cm.

Show answer
Radius = (28)/(2) = 14 cm. Area of sector = (1)/(2) × l × r = (1)/(2) × 22 × 14 = 154 cm².

CBSE 2027 sample paper · 3 marks

AX, AY and BC are tangents to the circle with P, R and Q respective point of contacts. Prove that AP = (1)/(2) (AB + BC + CA) (A is a point outside the circle. B lies on AX between A and P, and C lies on AY between A and R; BC touches the circle at Q.)

Show answer
Lengths of tangents drawn from an external point to a circle are equal, so BQ = BP, CQ = CR and AP = AR. AB + BC + CA = AB + BQ + CQ + AC = AB + BP + CR + AC = AP + AR (since AB + BP = AP and AC + CR = AR) = 2AP (as AP = AR) Hence AP = (1)/(2) (AB + BC + CA).

CBSE 2027 sample paper · 4 marks

An Art and craft teacher prepared a fan which looked like the sector of a circle using ice-cream sticks and black sheet as described below: (The fan is a sector of a circle of radius 10 cm. The part near the centre, where the ice-cream sticks show, is a sector of radius 4 cm; the black sheet covers the rest of the sector, the region between radius 4 cm and radius 10 cm.) (i) The angle subtended at the centre of the sector is 60°. Find the area of one face of the fan. (1) (ii) With the given sector angle of 60° at the centre, find area of black sheet used in the fan. (1) (iii)(A) The boundary of the black sheet region on one face is to be covered by a designer tape. What length of tape is required? (2) OR (iii)(B) If 29.6 cm of designer tape is required to cover the boundary of the black sheet region on one face of the fan, then evaluate the central angle of the sector. (2)

Show answer
θ = 60°, r = 4 cm, R = 10 cm. (i) Area of one face of the fan = (θ)/(360)π R2 = (60)/(360) × (22)/(7) × 102 = (1100)/(21) ≈ 52.38 cm². (ii) Area of black sheet = (θ)/(360)π(R2 - r2) = (60)/(360) × (22)/(7) × (100 - 16) = 44 cm². (iii)(A) Boundary of the black sheet region = two straight edges + outer arc + inner arc = 2(10 - 4) + (60)/(360) × 2 × (22)/(7)(10 + 4) = 12 + (44)/(3) = (80)/(3) cm (≈ 26.67 cm). OR (iii)(B) $2(10 - 4) + \frac{\theta}{360} \times 2 \times \frac{22}{7}(10 + 4) = 29.6 \Rightarrow \frac{\theta}{360} \times 88 = 17.6 \Rightarrow \theta = \frac{17.6 \times …