Tangent to a Circle

In Figure 3, a right triangle ABC, circumscribes a circle of radius r. If AB and BC are of lengths of 8 cm and 6 cm respectively, find the value of r.

In following figure , the incircle of Δ ABC , touches the sides BC , CA and AB at D , E and F respectively. Show AF + BD + CE = AE + BF + CD

In the above figure, seg AB and seg AD are tangent segments drawn to a circle with centre C from exterior point A, then prove that: ∠A = `1/2` [m(arc BYD) - m(arc BXD)]

If O is centre of a circle and Chord PQ makes an angle 50° with the tangent PR at the point of contact P, then the angle subtended by the chord at the centre is ______.

In the given diagram RT is a tangent touching the circle at S. If ∠PST = 30° and ∠SPQ = 60°, then ∠PSQ is equal to ______.

A circle can have ______ parallel tangents at the most.

In the given figure, diameter AB and chord CD of a circle meet at P. PT is a tangent to the circle at T. CD = 7.8 cm, PD = 5 cm, PB = 4 cm. Find the length of tangent PT.

In the given figure, O is the centre of the circle. PQ is a tangent to the circle at T. Chord AB produced meets the tangent at P.

AB = 9 cm, BP = 16 cm, ∠PTB = 50° ∠OBA = 45°

Find:

1. Length of PT 
2. ∠BAT
3. ∠BOT
4. ∠ABT