Q) In the given figure, EA/EC = EB/ ED , prove that ΔEAB ~ ΔECD Ans: Step 1: It is given that: ∴ by cross multiplying, we can say that: Step 2: Let’s look at Δ EAB and Δ ECD: ∠ AEB = ∠ DEC (∵ Vertically Opposite Angles) Step 3: Let’s compare Δ EAB […]
In the given figure, EA/EC = EB/ ED , prove that ΔEAB ~ ΔECD Read More »
Q) Prove that the tangents drawn at the end points of a chord of a circle makes equal angles with the chord. Ans: Let’s start by making a diagram for the question: Here, we have circle with Centre O and PQ is a chord. From point R, two tangents are drawn at end points of
Prove that the tangents drawn at the end points of a chord of a circle makes equal Read More »
Q) A stable owner has four horses. He usually tie these horses with 7 m long rope to pegs at each corner of a square shaped grass field of 20 m length, to graze in his farm. But tying with rope sometimes results in injuries to his horses, so he decided to build fence around the
A stable owner has four horses. He usually tie these horses with 7 m long rope to pegs Read More »
Q) In the given figure, AB and CD are tangents to a circle centred at O. Is angle BAC = angle DCA ? Justify your answer. Ans: VIDEO SOLUTION STEP BY STEP SOLUTION Step 1: Let’s connect center O with points A and C Step 2: Since BA is the tangent to the circle and
Q) In the given figure, PQ is tangent to a circle centred at O and ∠BAQ = 30°; show that BP = BQ. Ans: Here, We need to prove that BP = BQ, it means we need to get ∠ BQP = ∠ BPQ Step 1: Let’s start with given diagram. Since AB is a straight
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
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. (i) To
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 ∠