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Form 3 Mathematics: Circles, Chords and Tangents Questions and Answers

Form 3 Mathematics: Circles, Chords and Tangents Questions and Answers

Lessons (23)

• 1.    The figure below represents the cross-section of a metal bar. The cross section is in the form of a major segment of the circle. M is the midpoint of AB and CM is perpendicular to AB. Given that AB=CM=8cm. Calculate the area of the cross section.
  8m 53s

• 2.    A chord AB of length 13 cm subtends an angle of #67^0# at the circumference of a circle center O. Find the radius of the circle.
  4m 2s

• 3.    In the figure below, O is the centre of the circle of radius 2.8cm. Angle AOB=#150^0#. Determine the area of the shaded segment.
  3m 30s

• 4.    In the figure below O is the centre of a circle whose radius is 8cm. BA and BC are tangents to the circle. PD is a diameter of the circle and AC is a chord of length 8cm. Angle ABC=#120^0#. ARC is an arc of a circle centre B and radius 4.6cm. Calculate the area of the shaded region.
  10m 44s

• 5.    The figure below shows two pulleys with centers A and B and of radii 10cm and 5cm respectively. S and R are contact points of the belt with the pulleys. The distance between the centers of the two pulleys is 50cm, and #angle#SAB=#84.26^0#. A belt is tied around the two pulleys as shown. Calculate the total length of the belt.
  7m 8s

• 6.    In the figure below AB is a tangent to the circle centre O and radius 12cm. the area of the triangle AOB is 120#cm^2#. OXB is a straight line. Calculate XB.
  3m 40s

• 7.    The figure below (not drawn to scale) shows a triangle ABC inscribed in a circle. AB =6cm, BC=9cm and AC=10cm. Calculate: (a) The radius of the circle (b) The area of the shaded parts.
  8m 7s

• 8.    In the figure below O is the center of a circle whose radius is 5cm. AB=8cm and #angle#AOB is obtuse angle. Calculate the area of the major segment.
  4m 21s

• 9.    The figure below represents a circle a diameter 28 cm with a sector subtending an angle of #75^0# at the center. Find the area of the shaded segment to 4 significant figures
  2m 23s

• 10.    The figure below represents a rectangle PQRS inscribed in a circle centre 0 and radius 17cm . PQ = 16cm. Calculate (a) The length PS of the rectangle (b) The angle POS (c) The area of the shaded region
  5m 57s

• 11.    In the figure below, BT is a tangent to the circle at B. AXCT and BXD are straight lines AX = 6cm, CT = 8cm, BX = 4.8 cm and XD = 5cm. Find the length of (a) XC (b) BT
  3m 42s

• 12.    Chords XY and PQ of a circle intersect at a point M inside the circle. Given that MX = 8cm, XY = 14cm and MP = 4cm, calculate the length of MQ.
  2m 33s

• 13.    The figure below shows two circles each of radius 7cm, with centers at X and Y. The circles touch each other at point Q. Give that AXD = BYC =# 120^0# and lines AB, XQY and DC are parallel, calculate the area of: a) Minor sector XAQD (Take ? #22/7#) b) The shaded regions.
  11m 36s

• 14.    The figure below shows a circle, center, O of radius 7cm. TP and TQ are tangents to the circle at points P and Q respectively. OT =25cm. Calculate the length of the chord PQ
  7m 18s

• 15.    In the figure below, PQR is an equilateral triangle of side 6 cm. Arcs QR, PR and PQ arcs of circles with centers at P, Q and R respectively. Calculate the area of the shaded region to 4 significant figures
  5m 14s

• 16.    In the figure below AB is a diameter of the circle. Chord PQ intersects AB at N. A tangent to the circle at B meets PQ produced at R. Given that PN = 14cm, NB = 4 cm and BR = 7.5 cm, calculate the length of: (a) NR (b) AN
  6m 17s

• 17.    In the figure below, AT is a tangent to the circle at A TB = #48^0#, BC = 5 cm and CT = 4 cm. Calculate the length AT.
  1m 31s

• 18.    (a) In the figure below, lines NA and NB represent tangents to a circle at points A and B. Use a pair of compasses and ruler only to construct the circle. (b) Measure the radius of the circle.
  8m 12s

• 19.    In the figure below, the tangent ST meets chord VU produced at T. Chord SW passes through the centre, O, of the circle and intersects chord VU at X. Line ST = 12 cm and UT =8cm (a) Calculate the length of chord VU. (b) If WX =3 cm and VX:XU= 2:3, find SX.
  4m 35s

• 20.    In the figure below OS is the radius of the circle centre O. Chord SQ and TU are extended to meet P and OR is perpendicular to QS at R. OS=61cm, PU=50cm, UT=40cm and PQ=30cm. (a) Calculate the length of: (i) QS (ii) OR (b) Calculate, correct to 1 decimal place: (i) The size of angle ROS (ii) The length of the minor arc QS.
  11m 36s

• 21.    An arc 11 cm long, subtends an angle of 70° at the centre of a circle. Calculate the length, correct to one decimal place, of a chord that subtends an angle of 90° at the centre of the same circle.
  4m 44s

• 22.    Using a ruler and a pair of compasses only, construct: (a) A triangle LMN in which LM = 5 cm, LN = 5.6 cm and MLN = #45^0# . (b) The circle that touches all the sides of the triangle
  8m 21s

• 23.    In the figure below, AB is a tangent to the circle, centre O and radius 6 cm. The arc AC subtends an angle of 60° at the centre of the circle. Calculate the area of the shaded region, correct to 1 decimal place.
  4m 36s