# 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 …

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 …

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 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 …

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 a diameter. If ∠POR = 130° and S is a point on the circle, find ∠1 +∠2 Ans: In the given diagram, it is given that: ∠ …

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 …

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 …

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