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Q) In the given figure, AB, BC, CD and DA are tangents to the circle with centre O forming a quadrilateral ABCD. Show that angle AOB+ angle COD = 1800 Ans: Let’s draw a diagram and connect O with all vertices of Quadrilateral ABCD and al touch points on its circumference: Let’s start with Δ […]
triangles
Q) In the figure, E is a point on side CB produced of an isosceles triangle ABC with AB = AC. If AD ⊥ BC and EF ⊥ AC, prove that Δ ABD ~ Δ ECF. Ans: Since Δ ABC is an isosceles triangle, hence AB = AC ∴ ∠ B = ∠ C ………..
In the figure, E is a point on side CB produced of an isosceles triangle ABC Read More »
Q) In ∆ ABC, altitudes AD and BE are drawn. If AD = 7 cm, BE = 9 cm and EC = 12 cm then, find the length of CD. Ans: VIDEO SOLUTION STEP BY STEP SOLUTION Step 1: Let’s start with making a diagram for the question: Step 2: Next, let’s compare Δ ADC
Q) In the given figure, ABCD is a quadrilateral. Diagonal BD bisects ∠ B and ∠ D both. Prove that: (i) Δ ABD ~ Δ CBD (ii) AB = BC Ans: VIDEO SOLUTION STEP BY STEP SOLUTION Given: (i) ABCD is a quadrilateral and (ii) BD is angle bisector of ∠ B and ∠ D.
Q) Diagonals AC and BD of a trapezium ABCD intersect at O, where AB || DC. If DO/OB = 1/2, then show that AB = 2CD Ans: Let’s make a diagram for the given question: In Δ AOB and Δ COD, ∠ ABO = ∠ CDO (being traversal alternate angles with AB ǁ CD) similarly ∠
Q) A circle with centre O and radius 8 cm is inscribed in a quadrilateral ABCD in which P, Q, R, S are the points of contact as shown. If AD is perpendicular to DC, BC = 30 cm and BS = 24 cm, then find the length DC. Ans: To find length of DC, we
Q) A backyard is in the shape of a triangle ABC with right angle at B. AB = 7 m and BC = 15 m. A circular pit was dug inside it such that it touches the walls AC, BC and AB at P, Q and R respectively such that AP = x m. Based
A backyard is in the shape of a triangle ABC with right angle at B. Read More »
Q) If Δ ABC ~ Δ DEF and AB = 4 cm, DE = 6 cm, EF = 9 cm and FD = 12 cm, find the perimeter of Δ ABC. Ans: Let’s start with the diagram for he given question: Step 1: Since we are given that Δ ABC ~ Δ DEF, ∴ Step 2:
Q) In a Δ ABC, D and E are points on the sides AB and AC respectively such that BD = CE. If ∠B = ∠C, then show that DE ǁ BC Ans: Let’s start with the diagram for he given question: Step 1: We are given ∠ B = ∠ C, ∴ AB = AC
Q) ABCD is a trapezium with AB ǁ DC. AC and BD intersect at E. If Δ AED ~ Δ BEC, then prove that AD = BC. Ans: Let’s start with the diagram for he given question: Step 1: We are given AB ǁ DC, hence let’s look at △AEB and △CED: Here we