Theorem - The tangent at any point of a circle is perpendicular to the radius through the point of contact.
In Figure 2, XP and XQ are two tangents to the circle with centre O, drawn from an external point X. ARB is another tangent, touching the circle at R. Prove that XA + AR = XB + BR ?
In Figure 5, a triangle PQR is drawn to circumscribe a circle of radius 6 cm such that the segments QT and TR into which QR is divided by the point of contact T, are of lengths 12 cm and 9 cm respectively. If the area of ΔPQR = 189 cm2, then find the lengths of sides PQ and PR.
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 .
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.
Prove that a diameter AB of a circle bisects all those chords which are parallel to the tangent at that point A .
Prove that the tangent drawn at the mid-point of an arc of a circle is parallel to the chord joining the end points of the arc.
If Δ ABC is isosceles with AB = AC and C (O, r) is the incircle of the ΔABC touching BC at L,prove that L bisects BC.