Q) PA and PB are tangents drawn to a circle of centre O from an external point P. Chord AB makes and angle of 30 with the radius at the point of contact. If length of the chord of 6 cm, find the length of the tangent PA and the length of the radius OA. Ans: […]
circles
Q) Find the area of the unshaded region shown in the given figure. Ans: Let’s redraw the diagram: As we can see in the diagram, in the center area: diameter of semicircle (2R) = side of the inside square (S) or S = 2R ………………. (i) Also we see that Side of larger square = Gap
Find the area of the unshaded region shown in the given figure. Read More »
Q) With vertices A, B and C of Δ ABC as centres, arcs are drawn with radii 14 cm and the three portions of the triangle so obtained are removed. Find the total area removed from the triangle. Ans: We know that the area made by an arc of θ angle is given by = r2
Q) From an external point P, two tangents, PA and PB are drawn to a circle with centre O. At a point E on the circle, a tangent is drawn to intersect PA and PB at C and D, respectively. If PA = 10 cm, find the perimeter of ∆PCD. Ans: Let’s draw a diagram and
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
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: Since OP is O’P OO’2 = OP2 + O’P2 = 62 + 82
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