Find distance of point from the axes. 2. Draw angle bisector for ∠PQR = 115°. 3. A side of an isosceles...

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1. Find distance of point from the axes.
2. Draw angle bisector for ∠PQR = 115°.
3. A side of an isosceles right angle triangle is x. Find its.
4. Activity: In figure 3.77 ray PQ touches the circle at point Q. PQ = 12, PR = 3. Find PS and RS.

SnapAndSolve AI · Accepted Answer

The distance of a point from the axes can be found using its coordinates. If the point is (x, y), the distance from the x-axis is |y| and from the y-axis is |x|.
To draw the angle bisector for ∠PQR = 115°, use a compass to mark equal arcs from point Q on lines PQ and QR. Then, from these intersection points, draw arcs that intersect each other. Draw a line from Q through this intersection point to bisect the angle.
In an isosceles right triangle, the sides are in the ratio 1:1:√2. If one side is x, the hypotenuse is x√2.
Since PQ is a tangent to the circle at Q, PS = PQ = 12 (tangent-segment theorem). To find RS, use the power of a point theorem: PR * PS = PQ². So, 3 * 12 = 12², RS = 12 - 3 = 9.

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Find distance of point from the axes. 2. Draw angle bisector for ∠PQR = 115°. 3. A side of an isosceles...

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