Lines & Angles - SSC

In a circle with centre O, PA and PB are tangents to the circle at point A and point B, respectively. C is a point on the major are AB. If ∠ACB = 50°, then find the measure of ∠APB.

• A.

  80°

• B.

  90°

• C.

  50°

• D.

  100°

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The tops of two poles of heights 18 m and 30.5 mare connected by a wire. If the wire makes an angle of 30° with the horizontal, what is the length (in m) of the wire?

• A.

  28

• B.

  20

• C.

  36

• D.

  25

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The length of the shadow on the ground of a tall tree of height 30 m is 10$\sqrt{3}$m. What is the angle (in degrees) of elevation of the sun?

• A.

  30

• B.

  15

• C.

  45

• D.

  60

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In the following figure, MN is a tangent to a circle with centre O at point A. If BC is a diameter and ∠ABC = 42°, then find the measure of ∠MAB.

​​​​​​​

• A.

  84°

• B.

  42°

• C.

  48°

• D.

  45°

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Two poles of heights 10 m and 17 m are fixed to a level ground. The distance between the bottom of the poles is 24 m. What is the distance (in m) between their tops?

• A.

  25

• B.

  24

• C.

  30

• D.

  27

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A kite flying at a height of 120 m is attached to a string which makes an angle of 60° with the horizontal. What is the length (in m) of the string?

• A.

  90$\sqrt{3}$

• B.

  75$\sqrt{3}$

• C.

  84$\sqrt{3}$

• D.

  80$\sqrt{3}$

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The bisector of ∠B in △ABC meets AC at D. If AB = 12 cm. BC = 18 cm and AC = 15 cm then the length of AD (in cm) is:

• A.

  5

• B.

  6

• C.

  12

• D.

  9

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An equilateral triangle ABC is inscribed in a circle with centre O. Dis a point on the minor are BC and ∠CBD = . Find the measure of ∠BCD.

• A.

  40°

• B.

  50°

• C.

  20°

• D.

  30°

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In a △ABC, points P, Q and R are taken on AB, BC and CA, respectively, such that BQ = PQ and QC = QR. If ∠BAC = 75°, what is the measure of ∠PQR (in degrees)?

• A.

  30

• B.

  40

• C.

  75

• D.

  50

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A 20 m long ladder rests against a wall so that the angle between the ladder and the wall is 30°. How far (in m) is the base of the ladder from the wall?

• A.

  10$\sqrt{3}$

• B.

  20

• C.

  10

• D.

  20$\sqrt{3}$

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In ∆ABC, ∠A = 66∘, BD ⊥ AC and CE ⊥ AB. BD and EC inrersect at P. The bisectors ∠PBC and ∠PCB meet at Q. What is the measure of ∠BQC?

• A.

  132°

• B.

  143°

• C.

  147°

• D.

  127°

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The sides AB and AC of △ABC are produced to points D and E. respectively. The bisectors of ∠CBD and ∠BCE meet at P. If ∠A = 88°, then the measure of ∠P is:

• A.

  46°

• B.

  56°

• C.

  51°

• D.

  61°

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A poster is on top of a building. A person is standing on the ground at a distance of 50 m from the building. The angles of elevation to the top of the poster and bottom of the poster are 45° and 30°, respectively. What is 200% of the height (in m) of the poster?

• A.

  $\frac{25}{3}$(3 - $\sqrt{3}$)

• B.

  $\frac{75}{3}$(3 - $\sqrt{3}$)

• C.

  $\frac{50}{3}$(3 - $\sqrt{3}$)

• D.

  $\frac{100}{3}$(3 - $\sqrt{3}$)

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AB is a chord of a circle with centre O. while PAQ is the tangent at A. R is a point on the mirror are AB. If ∠BAQ = 70°, then find the measure of ∠ARB.

• A.

  110°

• B.

  125°

• C.

  70°

• D.

  145°

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In △ABC , D is a point on side BC such that ∠ADC = ∠BAC. If CA = 15 cm and CD = 9 cm, then CB (in cm) =?

• A.

  25

• B.

  15

• C.

  10

• D.

  12

• View Answer

In the given figure, O is the centre of the circle. ∠PDQ = 54°. What is the measure (in degree) of ∠PRQ?

​​​​​​​

• A.

  153

• B.

  207

• C.

  235

• D.

  137

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In a quadrilateral ABCD, the bisectors of ∠C and ∠D meet at point E. If ∠CED = 57° and ∠A = 47°, then the measure of ∠B is:

• A.

  47°

• B.

  67°

• C.

  77°

• D.

  57°

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In △ABC,∠A = 88°. If I is the incentre of the triangle, then the measure of ∠BIC is:

• A.

  112°

• B.

  134°

• C.

  56°

• D.

  68°

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In a circle with centre O, chords PR and QS meet at the point T, when produced, and PQ is a diameter. If ∠ROS = 42° then the measure of ∠PTQ is

• A.

  59°

• B.

  58°

• C.

  48°

• D.

  69°

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What is the angle of elevation of the sun when the shadow of a 9-m high pole is 3$\sqrt{3}$ m long?

• A.

  45°

• B.

  90°

• C.

  60°

• D.

  30°

• View Answer

AB is a chord of a circle with centre O.C is a point on the circumference of the circle in the minor sector. If ∠ABO = 40°. what
is the measure (in degree) of ∠ACB?

• A.

  110°

• B.

  100°

• C.

  130°

• D.

  120°

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AB is a diameter of a circle with centre O. The tangent at a point C on the circle and AB. when produced, meet at the point P. If
∠APC = 38°, when what is the measure of ∠PCB?

• A.

  23°

• B.

  26°

• C.

  29°

• D.

  19°

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From the top of a 195-m high cliff, the angles of depression of the top and bottom of a tower are 30° and 60°, respectively. Find the height of the rower (in m).

• A.

  195$\sqrt{3}$

• B.

  195

• C.

  130

• D.

  65

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The length of the shadow on the ground of a tall tree of height 45 m is 15$\sqrt{3}$ m. What is the angle (in degrees) of elevation of the sun?

• A.

  90°

• B.

  45°

• C.

  30°

• D.

  60°

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The sides PQ and PR of △PQR are produced to points S and T, respectively. The bisectors of ∠SQR and ∠TRQ meet at point U. If ∠QUR = 69°, then the measure of ∠P is:

• A.

  21°

• B.

  31°

• C.

  69°

• D.

  42°

• View Answer