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 whichtouches 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 right angle […]
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) A pendulum swings through an angle of 30and describes an arc of 8.8 cm in length. Find the length of the pendulum. Ans: 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) 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: 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) 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) 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