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Q) Find the area of the shaded region in Figure, where arcs drawn with centres A, B, C and D intersect in pairs at mid-points P, Q, R and S of the sides AB, BC, CD and DA respectively of a square ABCD. (Use Ï€ = 22/7) Ans: We are given that an arc is drawn […]
circles
Q) If a, b and c are the sides of a right angled triangle, where c is hypotenuse, then prove that the radius of the circle which touches the sides of the triangle is given by r = Ans: Let’s consider a right angled triangle ABC with sides a, b & c. Its ∠A is
If a, b and c are the sides of a right angled triangle, where c is hypotenuse, Read More »
Q) In figure, PQ is a tangent from an external point P to a circle with centre O and OP cuts the circle at T and QOR is adiameter. If ∠POR = 130° and S is a point on the circle, find ∠1 +∠2 Ans: In the given diagram, it is given that: ∠POR
In figure, PQ is a tangent from an external point P to a circle with centre O Read More »
Q)Â A pendulum swings through an angle of 30and describes an arc of 8.8 cm in length. Find the length of the pendulum. Ans:Â Let’s draw a diagram and plot the given information. (Note: your question will become clearer and your answer will never be wrong if you draw a diagram) We know that the circumference of
Q)Â A horse is placed for grazing inside a rectangular field 70 m by 52 m and is tethered to one corner by a rope 21 m long. On how much area can it graze? Ans:Â Let’s draw a diagram and plot the given information. (Note: your question will become clearer and your answer will never be
Q) Prove that the tangents drawn at the ends of a diameter of a circle are parallel. Ans: Let AB and CD are the 2 lines. Since, line AB is tangent to the circle at point P, therefore ∠APO = 90° (angle between radius and tangent) Similarly, line CD is tangent to the circle at
Prove that the tangents drawn at the ends of a diameter of a circle are parallel. Read More »
Q) In the given figure, PQ is a chord of the circle centered at O. PT is a tangent to the circle at P. If ∠QPT = 55°, Find the ∠PRQ. Ans: Since ∠OPT = 90° (angle between radius and tangent) and ∠QPT = 55° ∴ ∠OPQ = ∠OPT
Q)Â 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:
Q)Â 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