In the adjoining figure, two tangents drawn from external point C to a circle with centre O touches the circel at the point P and Q respectively. A tangent drawn at another point R of the circle intersects CP and CQ at the points A and B respectively. If CP = 7 cm and BC =11 cm, then determine the length of BR.

Explanation

Let us join O, P ,O , R and O, B.
Now in the circle with centre O, CP and CQ are two tangents from an external point C.
`therefore CP = CQ`
`therefore CQ =11 cm [because CP =11 cm ` (given)]
Again, given that `BC =7` cm
`thereforeBQ=CQ -BC`
`=11cm -7cm =4 cm`
Now, in `Delta BOQ and DeltaBOR, OQ =OR,[because` radii of same circle]
`angle OQB =angle ORB[because` each is right angles]
and hypotenuse OB is common to both.
`therefore DeltaBOQ-=Delta BOR` [by the R-H-S condition of cangruency]
`therefore BQ =BR[because ` similar sides of congruent triangles]
But `BQ =4 cm, therefore BR =4 cm.`