Question

PQ is a diameter of the circle PTQ. PR and QS are prependicular from P and Q ato
tangent at T. Show that PR + QS = PQ​

Answer 1

Answer:

In triangle ACO

OA = OC (Radii of the same circle) Therefore,

Triangle ACO is an isosceles triangle.

angle CAB = 30° (Given)

angle CAO = ACO 30° (angles opposite to equal sides of an isosceles triangle are equal)

angle PCO=90(radius is drawn at the point of contact is perpendicular to the tangent)

Now

angle PCA = angle PCO - angle CAO

Therefore,

Angle PCA =90°- 30°= 60 ....