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Maharashtra SSC Class 10 Geometry June 2026 question paper

Maximum marks 40 · Time 2 hours

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Q.1 (A)

1 mark each

  1. Q.1 (A) (1)1 mark
    Out of the following which is a Pythagorean triplet?

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  2. Q.1 (A) (2)1 mark
    What is the measure of semicircular arc of a circle?

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  3. Q.1 (A) (3)1 mark
    What is the equation of Y-axis?

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  4. Q.1 (A) (4)1 mark
    Radius of a sector of a circle is 3535 cm and length of its arc is 2222 cm. What is the area of the sector?

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Q.1 (B)

1 mark each

  1. Q.1 (B) (1)1 mark
    Find the diagonal of square whose side is 55 cm.
  2. Q.1 (B) (2)1 mark
    In the following figure, seg AE ⊥\perp seg BC, seg DF ⊥\perp line BC, AE=4AE = 4, DF=6DF = 6, then find A(△ABC)A(△DBC)\dfrac{A(\triangle ABC)}{A(\triangle DBC)}.
  3. Q.1 (B) (3)1 mark
    In the following figure, ray PQ touches the circle at point Q, PQ=12PQ = 12, PR=9PR = 9. Find PS.
  4. Q.1 (B) (4)1 mark
    Angle made by the line with the positive direction of X-axis is 30∘30^\circ. Find slope of the line.

Q.2 (A)

2 marks each · attempt any 2

  1. Q.2 (A) (1)2 marks
    In the following figure, chord EN and chord FS intersect each other at point M in the exterior of the circle. If m(arc NS)=125∘m(\text{arc NS}) = 125^\circ, m(arc EF)=37∘m(\text{arc EF}) = 37^\circ, then complete the following activity to find ∠NMS\angle NMS.
  2. Q.2 (A) (2)2 marks
    If sin⁡θ=2029\sin\theta = \dfrac{20}{29}, then complete the following activity to find cos⁡θ\cos\theta.
  3. Q.2 (A) (3)2 marks
    In the following figure, point O is the centre of the circle, ∠AOB=100∘\angle AOB = 100^\circ. Complete the following activity with the help of given figure.
    Type of arcName of the arcMeasure of the arc
    Minor arc
    Major arc

Q.2 (B)

2 marks each · attempt any 4

  1. Q.2 (B) (1)2 marks
    In the following figure, in △PQR\triangle PQR, seg RS bisects ∠R\angle R. If PR=15PR = 15, QR=20QR = 20, PS=12PS = 12, then find QS.
  2. Q.2 (B) (2)2 marks
    Find the length of diagonal of a rectangle whose length is 3535 cm and breadth is 1212 cm.
  3. Q.2 (B) (3)2 marks
    In the following figure, point G, D, E, F are concyclic points of a circle with centre C. ∠ECF=70∘\angle ECF = 70^\circ, m(arc DGF)=200∘m(\text{arc DGF}) = 200^\circ. Find m(arc DE)m(\text{arc DE}).
  4. Q.2 (B) (4)2 marks
    Find the distance between the points P(−1,1)P(-1, 1) and Q(5,−7)Q(5, -7).
  5. Q.2 (B) (5)2 marks
    A person is standing at a distance of 8080 m from a Church looking at its top. The angle of elevation is of 45∘45^\circ. Find the height of the Church.

Q.3 (A)

3 marks each · attempt any 1

  1. Q.3 (A) (1)3 marks
    In the following figure, in △ABC\triangle ABC ray BD bisects ∠ABC\angle ABC, A-D-C, seg ED ∥\parallel side BC, A-E-B, then to prove that ABBC=AEEB\dfrac{AB}{BC} = \dfrac{AE}{EB}, complete the following activity.
  2. Q.3 (A) (2)3 marks
    If P is the midpoint of segment joining the points A(−4,2)A(-4, 2) and B(6,2)B(6, 2), then complete the following activity to find the co-ordinates of point P.

Q.3 (B)

3 marks each · attempt any 2

  1. Q.3 (B) (1)3 marks
    In △PQR\triangle PQR, point S is the midpoint of side QR. If PQ=11PQ = 11, PR=17PR = 17, PS=13PS = 13, find QR.
  2. Q.3 (B) (2)3 marks
    Prove that, opposite angles of a cyclic quadrilateral are supplementary.
  3. Q.3 (B) (3)3 marks
    Draw a circle of radius 3.33.3 cm. Draw a chord PQ of length 6.66.6 cm. Draw tangents to the circle at point P and Q. Write your observation about the tangents.
  4. Q.3 (B) (4)3 marks
    In the following figure if A(P-ABC)=154A(P\text{-}ABC) = 154 cm2^2, radius of the circle is 1414 cm, find: (a) m∠APCm\angle APC, (b) l(arc ABC)l(\text{arc ABC}).

Q.4

4 marks each · attempt any 2

  1. Q.4 (1)4 marks
    In the following figure, line ll intersects side AB and side AC of △ABC\triangle ABC in points P and Q respectively. Show that A(△APQ)A(△ABC)=AP×AQAB×AC\dfrac{A(\triangle APQ)}{A(\triangle ABC)} = \dfrac{AP \times AQ}{AB \times AC}.
  2. Q.4 (2)4 marks
    Draw a circle having radius 33 cm. Draw chord XY=5XY = 5 cm. Draw tangents to a circle at point X and Y without using centre.
  3. Q.4 (3)4 marks
    Find the number of coins of 2.22.2 cm diameter and 0.20.2 cm thick, can be made by melting a metallic right circular cylinder of height 0.20.2 m and diameter 8.88.8 cm.

Q.5

3 marks each · attempt any 1

  1. Q.5 (1)3 marks
    AB is a chord of a circle with centre O. AC is a diameter of a circle. Line AT is a tangent at A. Write the answers of the following questions: (a) Draw the figure using the given information. (b) Find the measure of ∠CAT\angle CAT. (c) Find the measure of ∠ABC\angle ABC.
  2. Q.5 (2)3 marks
    α\alpha is acute angle. If 3sin⁡α−4cos⁡α=03\sin\alpha - 4\cos\alpha = 0, then find the values of tan⁡α\tan\alpha and sec⁡α\sec\alpha.