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asked May 23 in Mathematics by Pieter Diamond (40,709 points) | 26 views
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asked May 23 in Mathematics by Pieter Diamond (40,709 points) | 32 views
\(O\) 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. In the diagram below \(A D\|E F\| B C\). Prove that \(A F \cdot B D=A C \cdot D F\). 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. \(G F E\) is a double chord and \(\hat{H}_{1}=75^{\circ}\)
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Given that the opposite angles of a cyclic quadrilateral are supplementary and Circle centre \(C\) with quad \(QUAD\), prove that \(\hat{Q}+\hat{A}=180^{\circ}\) A big dart board consists of three concentric disks of radius 1,2, and 3 feet. If a dart lands in the center disk you get 50 points. If it lands in the middle ring you get 25 points, while if it lands in the outer ring you get 10 points.
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In the figure, three circles are tangent to each other and to the parallel lines as shown. If $C_{1}$ has radius $r$ and $C_{2}$ has radius $s$, what is the radius of $C_{3}$ ?
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In the diagram, $\mathrm{O}$ is the centre of the circle. TAS is a tangent to the circle at $\mathrm{A}$, $\mathrm{BA} \hat{\mathrm{S}}=40^{\circ}$ and $\mathrm{OBC}=54^{\circ}$ The cone is cut open to make a sector $ABC$ of a circle centre $O$ as shown in the diagram.
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Find the value of $\mathrm{x}$, if $A \hat{D} C$ and $A \hat{B} D$ are right angles.
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asked May 8, 2021 in Mathematics by MathsGee Platinum (122,714 points) | 158 views
In the diagram below, $\mathrm{O}$ is the centre of the circle. $\mathrm{BD}$ is a diameter of the circle.
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In the diagram below, $PQ$ is the diameter of circle $PQRS$ with centre $M$. $TS$ is the tangent to the circle at point $S$.
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asked Apr 30, 2020 in Mathematics by MathsGee Platinum (122,714 points) | 132 views
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asked Apr 30, 2020 in Mathematics by MathsGee Platinum (122,714 points) | 163 views
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asked Apr 30, 2020 in Mathematics by MathsGee Platinum (122,714 points) | 243 views
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asked Apr 28, 2020 in Mathematics by MathsGee Platinum (122,714 points) | 278 views

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