PYQ Vault

Day 49: MH SSC Class 10 Geometry

5 questions. Try each one first, then open its answer.

  1. Question 1

    Similarity. Asked once: Mar 2022

    Q2(A)(i)
    In the figure, seg AC and seg BD intersect each other at point P. If APCP=BPDP\dfrac{AP}{CP} = \dfrac{BP}{DP}, then complete the following activity to prove △ABP∼△CDP\triangle ABP \sim \triangle CDP.

  2. Question 2

    Circle. Asked once: Mar 2022

    Q2(B)(ii)
    In the figure, m(arc DXE)=105∘m(\text{arc } DXE) = 105^\circ, m(arc AYC)=47∘m(\text{arc } AYC) = 47^\circ, then find the measure of ∠DBE\angle DBE.

  3. Question 3

    Pythagoras Theorem. Asked once: Mar 2017

    Q3(i)
    Prove that: If the angles of a triangle are 45∘−45∘−90∘45^\circ - 45^\circ - 90^\circ, then each of the perpendicular sides is 12\dfrac{1}{\sqrt{2}} times the hypotenuse.

  4. Question 4

    Similarity. Asked once: Mar 2020

    Q3(A)(i)
    In the given figure, XX is any point in the interior of the triangle DEF. Point XX is joined to the vertices of the triangle. seg PQ∥PQ \parallel seg DE, seg QR∥QR \parallel seg EF (with PP on XD, QQ on XE, RR on XF). Prove that seg PR∥PR \parallel seg DF.

  5. Question 5

    Circle. Asked once: Mar 2022

    Q1(B)(ii)
    Chord AB and chord CD of a circle with centre O are congruent. If m(arc AB)=120∘m(\text{arc } AB) = 120^\circ, then find the m(arc CD)m(\text{arc } CD).