AB and AC are two chords of a circle of radius r such that AB = 2AC. If p and q are the distances of AB and AC from the centre, prove that 4g = p² +3r %3D

Q: Part (a) Evaluate 100e dz, where C'is the polygonal path consisting of the line segments from z =…

A: Since you have asked multiple questions, we will solve first question for you. For other question,…

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A: Since, we have been given that two chords PQ and RS of a circle withcentre O are produced to meet…

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A: The area of a sector is given by the formula πr2θ360° where r is the radius of the circle and θ.

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Q: Prove that the circle {(x, y), x² + y? = 1} is not homeomorphic to the interval [-1, 1).

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Q: (b) Prove that the perpendicular bisector of a chord of a circle passes through the centre.

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Q: The midpoint of AB is at (5, 0). If A = (4, 3), find B. B is:(

A: Consider the given information.

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A: The   distance from point Px,y  to 3,0 is 2 times the distance from point Px,y  to 0,2. Solution:…

Q: AB is the common chord of o0 and oQ. A If AB = 18 and each circle has a radius of length 15, how…

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Q: 3. Consider an acute angled triangle ABC and a point D on BC. Find points (by construction) E on AC…

A: Given:      An acute angled triangle ,inscribe in it a triangle whose perimeter is minimum.…

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Q: Determine the measure of the interior angle at vertex F. 4x 4x 4x 4x 2х 2x F A OA. 54 Ов. 36 Ос. 108…

A: Interior angles polygon is given

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Q: Let AB be a segment and letr be its axis. Show that every point P on r is equidistant from A and B.

A: Consider a line segment AB and r be its axis. To show every point P on the axis r is equidistant…

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A: We have to find radius

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Q: In the figure at the right, WY bisects UV at Y and UY bisects TW at X. For each situation, find the…

A: WY¯ bisects uv at y= UV¯ = YV¯---(1)UY bisects TW at x¯ wx =Tx ----(2)b) UY¯ = 4x -3YV¯ = X from…

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A: Given: A(-1, 2) and B(7, 14) To find: The coordinates of the point P on the directed line segment…

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A: Sum of angels in a triangle is 180°.

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A: We need to construct points.

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A: The given equation of lines of parallelogram are  ax + by + p = 0,   ax + by + q =0 m1 = -a/b c1 = -…

Q: Demonstrate that the circles (x – 2)? + y² = 2 and x? + (y – 2)2 = 2 share tangent at point (1, 1),…

A: Here we will apply the concept of finding the equation of tangent to the two circles at point (1,1).

Q: If the four straight lines ax + by + p= 0, ax+ by +q= 0, cx+ dy +r=0 |(p-g)(r-s)| and cx + dy + s =…

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Q: Evaluate f 3z2dz over C, where C is the upper half circle |z – connects points O and 1+i. -글히 %3D플…

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Q: The midpoint of AB is at (2,5). If A=(7,0) find B

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Q: Find the value of x that would prove this is an isosceles trapezoid. Then find each segment length.…

A: x=8.   the explanation is given in below step

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A: Given: A rod of length a unit slides on the x-axis and another rod of length b unit slides on the…

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A: The dilation factor is 3 Let the new coordinates be A'B'C' Then the new coordinates will be…

Q: If the four straight lines ax + by +p = 0,ax + by +q = 0,cx +dy + r = 0 |(p-q)(r-s)| and cx + dy +s…

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Q: A ABC is right-angled at A and has AB < AC. Point D is on BC so that AB = AD. Point L is the…

A: answer is in next step

Q: 5. If two chords in circle O, MN and XY, intersect at P then ZMPX = 2( MX + NY). 6. If two chords…

A: 5. The given statement is false .

Q: (a) Prove that curves a, ß: I → R² are congruent if k̟ = Kg and they have the same speed.

A: Part (a):   If any two continuous function defined on the interval I, and the two curves are…

Q: By Green's theorem, if C is the circle z+y =D4 taken anticlockwise, then 'dy, equals

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Q: 3. Let r be the radius of the circle inscribed in a right triangle with legs a and b and hypotenuse…

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Q: Given4ABC, let P,Q, andR be points on sides BC,AC, andAB, respectively, with RQ∦BC, and so that…

A: Consider the equation

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Q: In a plane, l lm and t 1 m. l and t related? By appearance, how are

A: We know that in a plane if l⊥m and t⊥m then l will be parallel to t So, l and t are related as l∥t

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Q: The image shows a circle with diameters AC and BD. Prove that chords BC and AD (not drawn) are…

A: Find your answer below

Q: Prove that if 0 < x < 2r, then a circle of radius r has a chord of length x. (You can do this using…

A: According to given ,only 1st solved....Radius of circle = r

Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.