PYQ Vault

Day 50: MH SSC Class 10 Geometry

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

  1. Question 1

    Pythagoras Theorem. Asked once: Mar 2016

    Q5(i)
    In the figure, AE=EF=AF=BE=CF=aAE = EF = AF = BE = CF = a and AT⊥BCAT \perp BC. Show that AB=AC=3 aAB = AC = \sqrt{3}\,a.

  2. Question 2

    Similarity. Asked once: Mar 2017

    Q5(i)
    In the given figure, AD is the bisector of the exterior ∠A\angle A of △ABC\triangle ABC. Seg AD intersects the side BC produced in D. Prove that BDCD=ABAC\dfrac{BD}{CD} = \dfrac{AB}{AC}.

  3. Question 3

    Circle. Asked once: Mar 2022

    Q4(ii)
    In the figure, seg AB and seg AD are tangent segments drawn to a circle with centre C from exterior point A, then prove that: ∠A=12[m(arc BYD)−m(arc BXD)]\angle A = \dfrac{1}{2}\left[m(\text{arc } BYD) - m(\text{arc } BXD)\right].

  4. Question 4

    Circle. Asked once: Mar 2020

    Q5(i)
    Circles with centres AA, BB and CC touch each other externally. If AB=3AB = 3 cm, BC=3BC = 3 cm, CA=4CA = 4 cm, then find the radii of each circle.

  5. Question 5

    Circle. Asked once: Mar 2019

    Solve the following questions (Any one):
    Q5(i)
    A circle with centre P is inscribed in △ABC\triangle ABC. Side AB, side BC and side AC touch the circle at points L, M and N respectively. The radius of the circle is r. Prove that A(△ABC)=12(AB+BC+AC)×rA(\triangle ABC) = \frac{1}{2}(AB + BC + AC) \times r.