Q) From an external point, two tangents are drawn to a circle. Prove that the line joining the external point to the centre of the circle bisects the angle between the two tangents. Ans: Step 1: Let’s draw a diagram with a circle of radius r and O as centre. Let the two tangents RP […]
circles
Q) Two concentric circle are of radii 5 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 angle between the two tangents drawn from an external point to a circle is supplementary to the angle subtended by the line segment joining the points of contacts at the centre. Ans: Step 1: Let’s draw a diagram with a circle of radius r and O as centre. Let the two
Q) ) In the given figure, O is the centre of the circle and QPR is a tangent to it at P. Prove that ∠QAP + ∠APR = 90°. Ans: VIDEO SOLUTION STEP BY STEP SOLUTION Since OA = OP (radii of same circle) In Δ OAP,  ∠OPA = ∠OAP .. (i)
Q) A car has two wipers which do not overlap. Each wiper has a blade of length 21 cm sweeping through an angle of 120°. Find the total area cleaned at each sweep of the two blades. Ans: Area cleaned by a blade = π r2 = x 21 x 21 x = x 21
Q) In the given figure, O is the centre of the circle. AB and AC are tangents drawn to the circle from point A. If ∠BAC = 65°, then find the measure of ∠BOC. Ans: Since ∠BAC + ∠BOC = 180° (circle’s identity) ∠BOC = 180° —∠BAC ∠BOC = 180°—
Q) The discus throw is an event in which an athlete attempts to throw a discus. The athlete spins anti-clockwise around one and a half times through a circle, then releases the throw. When released, the discus travels along tangent to the circular spin orbit. In the given figure, AB is one such tangent to
Q) In the given figure, a circle is inscribed in a quadrilateral ABCD in which ∠B = 900. If AD = 17 cm, AB = 20 cm and DS = 3 cm, then find the radius of the circle. Ans: In the above diagram, DR = DS = 3 cm Therefore, AR = AD –
Q) Two tangents TP and TQ are drawn to a circle with centre 0 from an external point T. Prove that ∠PTQ = 2∠OPQ. Ans: TP = TQ ⇒ ∠TPQ = ∠TQP Let ∠PTQ be θ ⇒ ∠TPQ = ∠TQP = = 90° –   Now, ∠OPT = 90° ⇒ ∠OPQ = 90° – [90° –