Q) In the given figure AC is the diameter of the circle with centre O. CD is parallel to BE. angle AOB = 80 deg and angle ACE = 20 deg . Calculate: (a) angle BEC (b) angle BCD (c) angle CED Ans: (a) ∠ BEC: Step 1: Given that ∠ AOB = 800 ∠ […]
circles
Q) In the given figure PT is a tangent to the circle. Chord BA produced meets the tangent PT at P. Given PT = 20cm and PA = 16cm. (a) Prove Δ ΡΤΒ ~ Δ ΡΑΤ (b) Find the length of AB. ICSE Specimen Question Paper (SQP)2025 Ans: a) Prove Δ ΡΤΒ ~ Δ ΡΑΤ:
Q) Varun has been selected by his School to design logo for Sports Day T-shirts for students and staff . The logo design is as given in the figure and he is working on the fonts and different colours according to the theme. In given figure, a circle with centre O is inscribed in a
Q) A Ferris wheel (or a big wheel in the United Kingdom) is an amusement ride consisting of a rotating upright wheel with multiple passenger-carrying components (commonly referred to as passenger cars, cabins, tubs, capsules, gondolas, or pods) attached to the rim in such a way that as the wheel turns, they are kept upright, usually
A Ferris wheel (or a big wheel in the United Kingdom) is an amusement ride consisting of Read More »
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,
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 »