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: Step 1: Let’s connect center O with points A and C Step 2: Since BA is the tangent to the circle and OA is the radius of the […]
triangles
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: (i) Let’s start with comparing Δ ADC and Δ BEC: ∠ ADC = ∠ BEC ( given AD and BE are altitudes hence both
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: (i) Let’s start with Δ ABD: ∠ BAD + ∠ ABD + ∠ BDA = 180 …. (i) Similarly in Δ BCD: ∠ BCD + ∠ DBC
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: