Q) A horse is tied to a peg at one corner of a square shaped grass field of side 15 m by means of a 5 m long rope. Find the area of that part of the field in which the horse can graze. Also, find the increase in grazing area if length of rope is […]
circles
Q) Two circles with centres O and O’ of radii 6 cm and 8 cm, respectively intersect at two points P and Q such that OP and O’P are tangents to the two circles. Find the length of the common chord PQ. Ans: Step 1: Since OP is O’P OO’2 = OP2 + O’P2 = 62
Two circles with centres O and O’ of radii 6 cm and 8 cm, respectively intersect at two Read More »
Q) A triangle ABC is drawn to circumscribe a circle of radius 4 cm such that the segments BD and DC are of lengths 10 cm and 8 cm respectively. Find the lengths of the sides AB and AC, if it is given that area ▲ ABC = 90 cm². Ans: Let’s join Point A, B,
Q) PT is the tangent to the circle centered at O. OC is Perpendicular to the chord AB. Prove that PA.PB = PC2-AC2. Ans: Let’s starts from LHS: PA . PB = (PC – AC) (PC + BC) Given that PC is to chord AB, therefore it bisects chord AB (by circle’s property) Hence, AC =
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
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: Let’s draw a diagram with a circle of radius r and O as centre. Let the two tangents RP
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°—