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Q) A circle is touching the side BC of a Δ ABC at the point P and touching AB and AC produced at points Q and R respectively. Prove that AQ = 1 (Perimeter of Δ ABC) Ans: Perimeter of the triangle Δ ABC, P = AB + AC + BC ∴ P = AB […]
A circle is touching the side BC of a A ABC at the point P and touching AB Read More »
Q) Find the area of the minor and the major sectors of a circle with radius 6 cm, if the angle subtended by the minor arc at the centre is 60 deg (Use pi = 3.14 ) Ans: Let’s draw the diagram for better understanding: Here, we are given that θ = 600, r =
Find the area of the minor and the major sectors of a circle with radius 6 cm, Read More »
Q) If a chord of a circle of radius 10 cm subtends an angle of 60 deg at the centre of the circle, find the area of the corresponding minor segment of the circle. (Use pi = 3.14 and sqrt(3) = 1.73 ) Ans: Let’s draw the diagram for better understanding:Â Step 1: Here, we
If a chord of a circle of radius 10 cm subtends an angle of 60 deg at the centre Read More »
Q) In a park, four poles are standing at positions A, B, C and D around the circular fountain such that the cloth joining the poles AB, BC, CD and DA touches the circular fountain at P, Q, R and S respectively as shown in the figure. Based on the above information, answer the following
Q) The perimeter of a certain sector of a circle of radius 5.6 m is 20.0 m. Find the area of the sector. Ans:Â Given that the radius = 5.6 m In a circle, perimeter of the sector is given by, P = 2 r + L Here, L is the arch length of a
Q) In the given figure, diameters AC and BD of the circle intersect at O. If ∠AOB = 60° and OA = 10 cm, then :(i) find the length of the chord AB.(ii) find the area of shaded region.(Take Ï€ = 3.14 and √3 = 1.73) Ï€ Ans: Let’s start with Δ AOB, ∠AOB
Q) In the given figure, AB is a diameter of the circle with centre O. AQ, BP and PQ are tangents to the circle. Prove that ∠POQ = 90°. Ans: Let’s connect Point O with Point R where tangent PQ touches the circle. Let’s consider ∠POR = x and ∠QOR = y Step 1:
In the given figure, AB is a diameter of the circle with centre O. AQ, BP and Read More »
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:Â 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 a hexagon ABCDEF circumscribes a circle, prove that AB + CD + EF = BC + DE + FA. (Q 31B – 30/2/2 – CBSE 2026 Question Paper) Ans: Let’s first draw a diagram for the given question: Let ABCDEF be the Heaxagon which is circumscribed on a circle. This circle has Center
If a hexagon ABCDEF circumscribes a circle, prove that AB + CD + EF = BC + DE + FA. Read More »