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 […]

# circles

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 »

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

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

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 »