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Aptitude miscellaneous
  1. In a circle with centre O, AB is a chord, and AP is a tangent to the circle. If ∠AOB = 140°, then the measure of ∠PAB is








  1. View Hint View Answer Discuss in Forum

    According to question , we draw a figure of a circle with centre O ,

    In ∆ OAB,
    Here , OA = OB = radius
    ∴ ∠OAB = ∠OBA
    ∴ ∠OAB + ∠OBA + ∠AOB = 180°
    ∴ 2∠OAB = 180° – 140° = 40°

    Correct Option: C

    According to question , we draw a figure of a circle with centre O ,

    In ∆ OAB,
    Here , OA = OB = radius
    ∴ ∠OAB = ∠OBA
    ∴ ∠OAB + ∠OBA + ∠AOB = 180°
    ∴ 2∠OAB = 180° – 140° = 40°

    ⇒ ∠OAB =
    40
    		 = 20°
    2

    ∴ ∠PAO = 90°
    ∴ ∠PAB = 90° – 20° = 70°

  1. Two circles with radii 25 cm and 9 cm touch each other externally. The length of the direct common tangent is








  1. View Hint View Answer Discuss in Forum

    On the basis of question we draw a figure of two circles with radii 25 cm and 9 cm touch each other externally.

    Here , r1 = 25 cm, r2 = 9 cm
    We find the required answer with the help of given formula ,
    Length of common tangent = √(distance between centres)² - (r1 - r2)²
    Length of common tangent = √(25 + 9)² - (25 - 9)²

    Correct Option: B

    On the basis of question we draw a figure of two circles with radii 25 cm and 9 cm touch each other externally.

    Here , r1 = 25 cm, r2 = 9 cm
    We find the required answer with the help of given formula ,
    Length of common tangent = √(distance between centres)² - (r1 - r2)²
    Length of common tangent = √(25 + 9)² - (25 - 9)²
    Length of common tangent = √(34)² - (16)²
    Length of common tangent = √(34 + 16)(34 - 16)
    Length of common tangent = √50 × 18 = 30 cm.

  1. ST is a tangent to the circle at P and QR is a diameter of the circle. If ∠RPT = 50°, then the value of ∠SPQ is








  1. View Hint View Answer Discuss in Forum

    According to question , we draw a figure of a circle with centre O ,

    Here , ∠RPT = 50°
    ∠RPQ = 90° (Angle of semi circle)

    Correct Option: A

    According to question , we draw a figure of a circle with centre O ,

    Here , ∠RPT = 50°
    ∠RPQ = 90° (Angle of semi circle)
    ∠TPS = 180°
    ∴ ∠SPQ = 180° – 50° – 90° = 40°

  1. The distance between the centres of two circles with radii 9 cm and 16 cm is 25 cm. The length of the segment of the tangent between them is








  1. View Hint View Answer Discuss in Forum

    On the basis of question we draw a figure of two circles with radii 9 cm and 16 cm ,

    Given that , r1 = 9 cm and r2 = 16 cm
    Distance between two centres = 25 cm
    ∴ Required length of tangent = √(Distance between two centres)2 - (r1 - r2)2
    Required length of tangent = √(25)² - (16 -9)²

    Correct Option: A

    On the basis of question we draw a figure of two circles with radii 9 cm and 16 cm ,

    Given that , r1 = 9 cm and r2 = 16 cm
    Distance between two centres = 25 cm
    ∴ Required length of tangent = √(Distance between two centres)2 - (r1 - r2)2
    Required length of tangent = √(25)² - (16 -9)²
    Required length of tangent = √625 - 49
    Required length of tangent = √576 = 24 cm

  1. DE is a tangent to the circumcircle of ∆ ABC at the vertex A such that DE|| BC. If AB = 17 cm, then the length of AC is equalto








  1. View Hint View Answer Discuss in Forum

    As per the given in question , we draw a figure

    DE || BC
    ∴ ∠DAB = ∠ABC
    ∠EAC = ∠ACB

    Correct Option: D

    As per the given in question , we draw a figure

    DE || BC
    ∴ ∠DAB = ∠ABC
    ∠EAC = ∠ACB
    Hence, ABC is equilateral triangle.
    ∴ side AB = AC = BC = 17 cm