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Recent questions tagged theorem

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A manufacturer of small motors is concerned with three major types of defects. If \(A\) is the event that the shaft size is too large, \(B\) is the event that the windings are improper, and \(C\)
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asked Jun 8 in Mathematics by MathsGee Platinum (122,654 points) | 19 views
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\(O\) is the centre of the circle with tangent \(B A\) and secant \(B C E\). \(O D=D E=D C\) and \(A O E\) is a straight line. \(O\) is the centre of circle with tangents \(K I\) and \(I T . O E I\) is a straight line. Prove the theorem of Pythagoras \(T P^{2}=P R^{2}+T R^{2}\)
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In the diagram below \(A D\|E F\| B C\). Prove that \(A F \cdot B D=A C \cdot D F\). In circle \(O, R Q \perp P M, O Q=Q N\) and \(x=\frac{M R}{M P}\). Calculate \(x\) Prove that \(A B D E\) is a cyclic quadrilateral given \(\hat{E}_{2}=x\).
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\(T R N\) is a tangent at \(R\) and \(S R=R Q\). If \(\hat{R}_{1}=x\), find five angles equal to \(x\). Given that the angle between a tangent to a circle and a chord drawn from the point of contact is equal to an angle in the alternate segment. Prove that \(\hat{A}_{1}=\hat{C}_{2}\) Given that two tangents drawn to a circle from the same point outside the circle are equal in length and tangents \(T P K\) and \(S R K\) to circle centre \(O\), prove that \(PK=RK\) Given that two tangents drawn to a circle from the same point outside the circle are equal in length and tangents \(T P K\) and \(S R K\) to circle centre \(O\).Prove that \(PK=RK\) \(A B C D\) is a parallelogram and \(B \hat{A} D=\hat{F}_{1}\). Prove that \(C E F G\) is a cyclic quad. Given that the opposite angles of a cyclic quadrilateral are supplementary and Circle centre \(C\) with quad \(QUAD\), prove that \(\hat{Q}+\hat{A}=180^{\circ}\) Given that the circle centre \(N\) with arc \(R T\) subtending \(R \hat{P} T\) and \(R \hat{M} T\) in the same segment. Prove that \(R \hat{P} T=R \hat{M} T\) Given that the perpendicular bisector of a chord passes through the centre of the circle and \(R T=R P\) and \(M R \perp T P\), prove that \(M R\) goes through the centre of the circle. Given that a line drawn from the centre of a circle perpendicular to a chord bisects the chord. Prove that \(NM=MP\)
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asked Mar 14 in Economics and Finance by Pieter Diamond (40,695 points) | 80 views
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asked Feb 20 in Mathematics by MathsGee Platinum (122,654 points) | 85 views
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asked Feb 20 in Mathematics by MathsGee Platinum (122,654 points) | 88 views
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asked Feb 20 in Mathematics by MathsGee Platinum (122,654 points) | 92 views
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asked Feb 20 in Mathematics by MathsGee Platinum (122,654 points) | 99 views
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