Q) In the given figure, a circle centered at origin O has radius 7 cm, OC is median of Δ OAB. Find the length of median OC. Ans: Step 1: In the given circle, OA and OB are the radii of the same circle and they intersect at 90 degrees (coordinates) Δ AOB, by Pythagoras […]
circles
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:Â 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) 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 Ï€ R ∴ Ï€ 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: 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