Q) In figure, a circle is inscribed in a Δ ABC having sides BC = 8 cm, AB = 10 cm and AC = 12 cm. Find the length BL, CM, and AN. Ans: Step 1: Let’s consider BL = X CL = BC – BL ∴ CL = 8 – X ………(i) Step 2: Since, […]
circles
Q) An arc of a circle of radius 10 cm subtends a right angle at the centre of the circle. Find the area of the corresponding major sector. (Use π = 3·14) Ans: The Area of an arc making θ angle at centre is given by: A = π r 2 x given the values as
Q) In the given figure, Δ ABC is circumscribing a circle. Find the length of BC, if AR = 4 cm, BR = 3 cm and AC = 11 cm. Ans: Step 1: We know that, the tangents on a circle from a point are equal Therefore, the tangents BP and BR, tangents to circle
Q) From an external point P, two tangents PA and PB are drawn to the circle with centre O. Prove that OP is the perpendicular bisector of chord AB. Ans: Step 1: Let’s draw a diagram with a circle with O as centre. Let the two tangents PA and PB are drawn from point A
Q) In the given figure, O is the centre of the circle. If Ð AOB = 145°, then find the value of x. Ans: Step 1: From the given diagram, ∠ AOB = 1450 ∴ Reflex angle ∠ AOB = 3600 – 1450 = 215 0 Step 2: By the subtended angle theorem, “The angle
Q) Prove that the parallelogram circumscribing a circle is a rhombus. Ans: Step 1: Let’s start by making a diagram for the given question: Here ABCD is a parallelogram and its is circumscribing a circle with center O. This parallelogram is touching the circle at points P, Q, R and S. Step 2: Let’s connect
Prove that the parallelogram circumscribing a circle is a rhombus. Read More »
Q) Two concentric circle are of radii 4 cm and 3 cm. Find the length of the chord of the larger circle which touches the smaller circle. Ans: Let’s draw a diagram with 2 concentric circles, both having O as centre. Let the radius of two circles be shown as OP = 3 cm of
Q) Prove that the lengths of tangents drawn from an external point to a circle are equal. Using above result, find the length BC of Δ ABC. Given that, a circle is inscribed in Δ ABC touching the sides AB, BC and CA at R, P and Q respectively and AB= 10 cm, AQ= 7cm
Prove that the lengths of tangents drawn from an external point to a circle are equal. 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 »