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Q) In figure 1, a right triangle ABC in which ∠B = 90 is shown. Taking AB as diameter, a circle has been drawn intersecting AC at point P. Prove that the tangent drawn at point P bisects BC. Ans: Here is the step by step solution method: Step 1: We can see that, Q is […]
circles
Q)Â PQRS is a diameter of a circle of radius 6 cm. The lengths PQ, QR and RS are equal. Semi-circles are drawn such that PQ = QR = RS. Semicircles are drawn on PQ and QS as diameters as shown in figure. Find the perimeter and area of the shaded region. Ans:Â Given that the
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 Ï€ = ) Ans: Let’s start with calculating area of triangles: In 1st triangle: sides a = 35 cm,
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 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