Question

draw a circle of radius 3.5 CM and construct a pair of tangent to it form a point 8 CM form the centre of circle measure the length of the tangent​

Answer 1

teps of construction:---

step 1:--Draw a circle of radius 3•5cm taking as a centre.

step 2:--Extend the diameter, on extended diameter take two points A and B in two directions,OA = OB=8cm.

step3:--Draw perpendicular bisector of OA, the bisector cuts OA at P.

step 4:--Draw perpendicular bisector of OB, the bisector cuts OB at Q.

step 5:--Taking P as center and radius equal to length OP or PA, draw a circle.

step 6:--Two circles intersect each other at K and L.

step 7:--join AK and AL, AK and AL are the required tangents from point A.

step 8:--Now taking Q as center and radius equal to length OQ or QB, draw a circle,

step 9:--The circle with centre O and centre Q intersect each other at M and N.

step 10:-- Join BM and BN, BM and BN are the required tangents from point B.

Answer 2

The length of tangent from the point it touches the circle to the starting point would be 7.19 cm

Consider the center of circle be point O and the starting point of tangent be P.

The tangent meets the circle at point A.

In the triangle PAO,

we can apply Pythagorean theorem since a tangent meets a circle at 90 degree angle:

OA² + AP² = OP²

(3.5)² + AP² = 8²

AP² = 51.75

AP = √51.75 = 7.19 cm