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 […]
circles
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) 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: We know that the perimeter of a circle’s sector making θ angle, is given by: P = 2 R + 2 π R ∴ π R = ……..(i) And the area
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: Step 1: Here, we are given that θ
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: 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: 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 π = 3.14 and √3 = 1.73) π Ans: Let’s start with Δ AOB, ∠ AOB