False Support: Allow us to attempt to build the figure as given in the inquiry. Steps of development, Define a boundary section \[BC.\] With \[B\text{ }and\text{ }C\]as focuses, draw two circular...
By geometrical construction, it is possible to divide a line segment in the ratio √3:(1/√3)
True Support: As per the inquiry, Ratio\[=\text{ }\surd 3\text{ }:\text{ }\left( \text{ }1/\surd 3 \right)\] On working on we get, \[\surd 3/\left( 1/\surd 3 \right)\text{ }=\text{ }\left( \surd...
If PA and PB are tangents from an outside point P. such that PA = 10 cm and ∠APB = 60°. Find the length of chord AB.
Given, $AP=10cm$ $\angle APB={{60}^{\circ }}$ According to the figure We know that, A line drawn from centre to point from where external tangents are drawn, bisects the angle made by tangents at...
In Fig below, PQ is tangent at point R of the circle with center O. If ∠TRQ = 30°, find ∠PRS
Given, $\angle TRQ={{30}^{\circ }}$ . At point R, OR ⊥ RQ. So, $\angle ORQ={{90}^{\circ }}$ $\Rightarrow \angle TRQ+\angle ORT={{90}^{\circ }}$ $\Rightarrow \angle ORT={{90}^{\circ...
Prove that the intercept of a tangent between two parallel tangents to a circle subtends a right angle at centre.
We are considering a circle with centre ‘O’ with two parallel tangents through A & B at ends of diameter. M intersect the parallel tangents at P and Q Then, required to prove: $\angle...
If AB, AC, PQ are the tangents in the figure, and AB = 5 cm, find the perimeter of ∆APQ
Since AB and AC are the tangents from the same point A ∴AB=AC=5cm Similarly, BP=PX and XQ=QC Perimeter of \[\Delta APQ=AP+AQ+PQ\] \[=AP+AQ+(PX+XQ)\] \[=(AP+PX)+(AQ+XQ)\] \[=(AP+BP)+(AQ+QC)\]...
A chord PQ of a circle is parallel to the tangent drawn at a point R of the circle. Prove that R bisects the arc PRQ.
Provided in question: Chord PQ is parallel to tangent at R.To prove: R bisects the arc PRQ. Proof: Since PQ || tangent at R. $\angle 1=\angle 2$ [alternate interior angles]$\angle 1=\angle 3$...
Out of the two concentric circles, the radius of the outer circle is 5 cm and the chord AC of length 8 cm is a tangent to the inner circle. Find the radius of the inner circle.
Suppose C1 and C2 are two circles with the same center O. And AC is a chord touching C1 at the point D let’s join OD.So, $OD\bot AC$$AD=DC=4cm$ [perpendicular line OD...
If the quadrilateral sides touch the circle, prove that sum of pair of opposite sides is equal to the sum of other pair.
Let’s Consider a quadrilateral ABCD touching circle with the centre O at points E, F, G and H as we can see in figure. We know that, In a circle with two points outside of it, the tangents drawn...
A point P is 26 cm away from O of circle and the length PT of the tangent drawn from P to the circle is 10 cm. Find the radius of the circle.
Given, OP = $26cm$ PT = tangent length = $10cm$ To find: radius = OT =$?$ We know that, Radius and tangent are perpendicular at the point of contact, $\angle OTP={{90}^{\circ }}$ $$ So,...