Q) Find upto three places of decimal the radius of the circle whose area is the sum of the areas of two triangles whose sides are 35, 53, 66 and 33, 56, 65 measured in centimeters (Use π = ) Ans: Let’s start with calculating area of triangles: In 1st triangle: sides a = 35 cm, […]
circles
Q) In the given figure, ABC is a triangle in which ∠B = 900, BC = 48 cm and AB = 14 cm. A circle is inscribed in the triangle, whose centre is O. Find radius r of in-circle. Ans: By Pythagorus theorem, AC = = = = 50 cm Method 1: OP = OQ (radius
In the given figure, ABC is a triangle in which ∠B = 90, BC = 48 cm and AB = 14 cm. Read More »
Q) A quadrilateral ABCD is drawn to circumscribe a circle, as shown in the figure. Prove that AB + CD = AD + BC Ans: By tangents property, we know that the tangents drawn on a circle from an external point are always equal, ∴ from Point A: AP = AS ………….. (i) from Point B:
Q) In the given figure, tangents PQ and PR are drawn to a circle such that ∠RPQ = 300. A chord RS is drawn parallel to tangent PQ. Find the ∠RQS. Ans: In △PRQ, PQ and PR are tangents from an external point P to circle. ∴ PR = PQ Since the angles opposites to equal sides
In the given figure, tangents PQ and PR are drawn to a circle such that ∠RPQ = 30 . Read More »
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 π = 22/7) Ans: We are given that an arc is drawn
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 »