Question

.
4. In figure 3.58, seg RS is a diameter of the
circle with centre o. Point T lies in
the exterior of the circle. Prove that
angle RTS is an acute angle.
Fig. 3.58​

Answer 1

POINT T IS EXTERIOR OF CIRCLE.

POINT O IS CENTRE OF CIRCLE.

SEGMENT RS IS DIAMETER.

CONSTRUCTION: DRAW SEGMENT RT AND TS.AND PS INTERSECT AT POINT P

ANGLE RPS=90 (ANGLE IN SEMICIRCLE IS RIGHT ANGLE)

SEGMENT PS IS PERPENDICULAR TO RT

ANGLE RPS=ANGLE TPS=90

NOW IN TRIANGLE TPS

SUM OF ALL ANGLE =180

(PROPERTY OR TRIANGLE)

.

.

ANGLE PTS=90-ANGLE PST

ANGLE RTS>90

ANGLE RTS IS AN ACUTE ANGLE

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